AP Statistics Test Booklet

AP STATISTICS Test Booklet 567 1. A fair six-sided die, with sides numbered 1 through 6, will be rolled a total of 15 times. Let represent the average represent the average of the remaining five rolls. What is the mean of the of the first ten rolls, and let ? sampling distribution of the difference in sample means (A) (B) (C) (D) (E) 2. According to government data, 22 percent of children in the United States under the age of 6 years live in households with incomes that are classified at a particular income level. A simple random sample of 300 children in the United States under the age of 6 years was selected for a study of learning in early childhood. If the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (Note: z represents a standard normal random variable.) (A) (B) (C) (D) (E) 3. A large city newspaper periodically reports the mean cost of dinner for two people at restaurants in the city. The newspaper staff will collect data from a random sample of restaurants in the city and estimate the mean price using a 90 percent confidence interval. In past years, the standard deviation has always been very close to $35. Assuming that the population standard deviation is $35, which of the following is the minimum sample size needed to obtain a margin of error of no more than $5 ? (A) 90 (B) 112 (C) 133 (D) 147 (E) 195 AP Statistics Page 1 of 86 Test Booklet 567 4. 5. A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer’s batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem? (A) The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30. (B) The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30. (C) The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30. (D) The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30. (E) The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30. An international polling agency estimates that 36 percent of adults from Country X were first married between the ages of 18 and 32, and 26 percent of adults from Country Y were first married between the ages of 18 and 32. Based on the estimates, which of the following is closest to the probability that the difference in proportions between a random sample of 60 adults from Country X and a random sample of 50 adults from Country Y (Country X minus Country Y) who were first married between the ages of 18 and 32 is greater than 0.15 ? (A) 0.1398 (B) 0.2843 (C) 0.4315 (D) 0.5685 (E) 6. 0.7157 Approximately 52 percent of all recent births were boys. In a simple random sample of 100 recent births, 49 were boys and 51 were girls. The most likely explanation for the difference between the observed results and the expected results in this case is (A) bias (B) variability due to sampling (C) nonsampling error (D) a sampling frame that is incomplete (E) 7. confounding A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds? Page 2 of 86 AP Statistics Test Booklet 567 (A) 0.1151 (B) 0.2743 (C) 0.7257 (D) 0.8849 (E) 8. Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated. A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone? (A) (B) (C) (D) (E) 9. A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. All 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. The process was repeated 20 times. Which of the following best describes the distribution being simulated? (A) A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 0.54 (B) A sampling distribution of a sample mean with n = 10, μx̄ = 3.5, and σx̄ ≈ 1.74 (C) A sampling distribution of a sample mean with n = 20, μx̄ = 3.5, and σx̄ ≈ 0.38 (D) A sampling distribution of a sample proportion with n = 10, μp̂ = 1/6, and σp̂ ≈ 0.118 (E) 10. A sampling distribution of a sample proportion with n = 20, μp̂ = 1/6, and σp̂ ≈ 0.083 For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? (A) A random sample of 8 taken from a normally distributed population (B) A random sample of 50 taken from a normally distributed population (C) A random sample of 10 taken from a population distribution that is skewed to the right (D) A random sample of 75 taken from a population distribution that is skewed to the left (E) 11. A random sample of 100 taken from a population that is uniform At a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. For samples of size 5, which of the following is the best interpretation of ? AP Statistics Page 3 of 86 Test Booklet 567 (A) The probability that each of the 5 backpacks selected will have a weight above 22 pounds is approximately 0.05. (B) The probability that each of the 5 backpacks selected will have a weight above 19.7 pounds is approximately 0.05. (C) The probability that the population mean is greater than 22 pounds is approximately 0.05. (D) For all samples of size 5, approximately 5% of the sample will have a probability greater than 22 pounds. (E) 12. For all samples of size 5, the probability that the sample mean will be greater than 22 pounds is approximately 0.05. Based on records kept at a gas station, the distribution of gallons of gas purchased by customers is skewed to the right with mean 10 gallons and standard deviation 4 gallons. A random sample of 64 customer receipts was selected, and the sample mean number of gallons was recorded. Suppose the process of selecting a random sample of 64 receipts and recording the sample mean number of gallons was repeated for a total of 100 samples. Which of the following is the best description of a dotplot created from the 100 sample means? (A) The dotplot is skewed to the right with mean 10 gallons and standard deviation 4 gallons. (B) The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.5 gallon. (C) The dotplot is skewed to the right with mean 10 gallons and standard deviation 0.4 gallon. (D) The dotplot is approximately normal with mean 10 gallons and standard deviation 0.5 gallon. (E) 13. The dotplot is approximately normal with mean 10 gallons and standard deviation 0.4 gallon. Researchers working for a certain airline are investigating the weight of carry-on bags. The researchers will use the mean weight of a random sample of 800 carry-on bags to estimate the mean weight of all carry-on bags for the airline. Which of the following best describes the effect on the bias and the variance of the estimator if the researchers increase the sample size to 1,300 ? (A) The bias will decrease and the variance will remain the same. (B) The bias will increase and the variance will remain the same. (C) The bias will remain the same and the variance will decrease. (D) The bias will remain the same and the variance will increase. (E) The bias will decrease and the variance will decrease. 14. A certain statistic is being used to estimate a population parameter What property does exhibit? (A) The sampling distribution of is normal. (B) The sampling distribution of is binomial. (C) The sampling distribution of is uniform. (D) is unbiased. (E) is biased. . The expected value of 15. Which of the following conditions will create a biased estimator of a population parameter? Page 4 of 86 AP Statistics is not equal to . Test Booklet 567 (A) The sampling distribution of the estimator is skewed to the left. (B) The sampling distribution of the estimator is skewed to the right. (C) The sampling distribution of the estimator is not the same shape as the distribution of the population parameter. (D) The expected value of the estimator is not equal to the population parameter. (E) 16. The variability of the sampling distribution of the estimator is not equal to the variability of the population parameter. At a large university, the division of computing services surveyed a random sample of 45 biology majors and 55 business majors from populations of over 1,000 biology and 1,000 business majors. The sampled students were represent the average hours asked how many hours they spend per week using any university computer lab. Let per week spent in any university computer lab by the 45 biology majors, and let represent the average hours per week spent in any university computer lab by the 55 business majors. Which of the following is the best explanation for why the sampling distribution of normal distribution? can be modeled with a (A) The two sample standard deviations are assumed to be equal. (B) The sample sizes are both sufficiently large. (C) The distributions of the population are normal. (D) The population standard deviations are assumed equal. (E) 17. There are at least 30 students in each of the two populations. A bag contains chips of which 27.5 percent are blue. A random sample of 5 chips will be selected one at a time and with replacement. What are the mean and standard deviation of the sampling distribution of the sample proportion of blue chips for samples of size 5 ? (A) The mean is , and the standard deviation is (B) The mean is 0.275, and the standard deviation is (C) The mean is 0.275, and the standard deviation is . . . (D) The mean is 27.5, and the standard deviation is (E) 18. The mean is 27.5, and the standard deviation is . . In two common species of flowers, A and B, the proportions of flowers that are blue are and , respectively. Suppose that independent random samples of 50 species-A flowers and 100 species-B flowers are selected. Let be the sample proportion of blue species-A flowers and be the sample proportion of blue species-B flowers. What is the mean of the sampling distribution of ? (A) (B) (C) (D) (E) AP Statistics Page 5 of 86 Test Booklet 567 19. Suppose the variance in trunk diameter of the giant sequoia tree species is , while the variance in trunk . Let represent the average trunk diameter of four diameter of the California redwood tree species is randomly sampled giant sequoia trees, and let represent the average trunk diameter of three randomly sampled California redwood trees. If the random sampling is done with replacement, what is the standard deviation of the sampling distribution of the difference in sample means ? (A) (B) (C) (D) (E) 20. Carly commutes to work, and her commute time is dependent on the weather. When the weather is good, the distribution of her commute times is approximately normal with mean 20 minutes and standard deviation 2 minutes. When the weather is not good, the distribution of her commute times is approximately normal with mean 30 minutes and standard deviation 4 minutes. Suppose the probability that the weather will be good tomorrow is 0.9. Which of the following is closest to the probability that Carly’s commute time tomorrow will be greater than 25 minutes? (A) 0.0056 (B) 0.0894 (C) 0.0950 (D) 0.8055 (E) 21. 0.9006 The distribution of prices for a certain car model is approximately normal with mean $21,800 and standard deviation $400. A random sample of 4 cars of the model will be selected. What is the correct unit of measure for the mean of the sampling distribution of ? (A) Dollars (B) Models (C) Cars (D) Samples (E) 22. There are no units associated with the mean of the sampling distribution. A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let represent the population proportion of all cell phone screens with a screen defect, therefore . For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample . Which of the following is the best interpretation of ? size 400, Page 6 of 86 AP Statistics Test Booklet 567 23. 24. (A) For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05. (B) For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05. (C) For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05. (D) For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05. (E) For all samples of size 400 from this population, the standard deviation of all resulting sample proportions of cell phone screens with a screen defect is 0.05. A national charity contacted 100 randomly selected people by phone, and 7 percent of those contacted made a donation to the charity. The population proportion of those who make a donation when contacted by phone is . For samples of size 100, which of the following best interprets the mean of the sampling known to be distribution of the sample proportion of people who make a donation when contacted by phone? (A) For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.05. (B) For all random samples of 100 people contacted by phone, the sample proportion of those who make a donation will be 0.07. (C) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.05. (D) The mean of all sample proportions of those who make a donation from all random samples of 100 people contacted by phone is 0.07. (E) The probability that the mean of the sampling distribution of sample proportions is greater than 0.07 is 0.05. Consider a population consisting of four children with ages, in years, of , , , and years, and the population variance is square years. . The population mean age is For simple random samples of size taken with replacement, what are the mean and standard deviation of the sampling distribution of the sample mean age, in years? 25. (A) Mean and standard deviation (B) Mean and standard deviation (C) Mean and standard deviation (D) Mean and standard deviation (E) and standard deviation Mean Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p̂? (A) n = 1,000 and p close to 0 (B) n = 1,000 and p close to 1 (C) n = 1,000 and p close to 1/2 (D) n = 100 and p close to 0 (E) n = 100 and p close to 1/2 AP Statistics Page 7 of 86 Test Booklet 567 26. On a given day, the proportion of workers from Company B who purchase a coffee from the company cafeteria is 0.62 and the proportion of workers from Company C who purchase a coffee from the company cafeteria is 0.71. A random sample of40 workers was selected from Company B and another random sample of 40 workers was selected and the from Company C. The proportion of workers from Company B who purchased coffee was proportion of workers from Company C who purchased coffee was . What is the correct unit of measure for the mean of the sampling distribution of ? (A) Days (B) Dollars (C) Companies (D) Workers (E) 27. There are no units associated with the mean of the sampling distribution. There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean? (A) Approximately normal with mean $206,274 and standard deviation $3,788 (B) Approximately normal with mean $206,274 and standard deviation $37,881 (C) Approximately normal with mean $206,274 and standard deviation $520 (D) Strongly right-skewed with mean $206,274 and standard deviation $3,788 (E) 28. Strongly right-skewed with mean $206,274 and standard deviation $37,881 At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean minutes and standard deviation minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than minutes for a random sample of customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size ? (A) Approximately normal with mean minutes and standard deviation minutes (B) Approximately normal with mean minutes and standard deviation minute (C) Approximately normal with mean minutes and standard deviation minutes (D) Binomial with mean (E) 29. Binomial with mean minutes and standard deviation minutes and standard deviation minutes minutes According to data from the United States Elections Project, only percent of eligible voters voted in the elections. For random samples of size , which of the following best describes the sampling distribution of , the elections? sample proportion of people who voted in the Page 8 of 86 AP Statistics Test Booklet 567 (A) The sampling distribution is skewed to the left, with mean 30. and standard deviation (B) The sampling distribution is skewed to the right, with mean (C) The sampling distribution is approximately normal, with mean and standard deviation . (D) The sampling distribution is approximately normal, with mean and standard deviation . (E) and standard deviation . The sampling distribution is approximately normal, with mean and standard deviation . . Two non-profit organizations, L and M, accept donations from people. In a certain month, 140 people donated to , and 42 people donated to organization M, with an organization L, with an average donation amount of average donation amount of . What is the correct unit of measure for the mean of the sampling distribution of ? (A) Donations (B) Months (C) People (D) Organizations (E) 31. Dollars Researchers are studying populations of two squirrels, the eastern gray and the western gray. For the eastern gray squirrel, about 22 percent of the population weighs over 0.5 kilogram . For the western gray squirrel, about 36 percent of the population weighs over 0.5 . A random sample of 60 squirrels will be selected from the population of eastern gray squirrels, and a random sample of 120 squirrels will be selected from the population of western gray squirrels. What is the mean of the sampling distribution of the difference in sample proportions (eastern minus western) ? (A) (B) (C) (D) (E) 32. The director of a marketing department wants to estimate the proportion of people who purchase a certain product online. The director originally planned to obtain a random sample of people who purchased the product. people. Which of the following However, because of budget concerns, the sample size will be reduced to describes the effect of reducing the number of people in the sample? (A) The variance of the sample will increase. (B) The variance of the population will decrease. (C) The variance of the sampling distribution of the estimator will increase. (D) The variance of the sampling distribution of the estimator will decrease. (E) The variance of the sampling distribution of the estimator will remain the same. AP Statistics Page 9 of 86 Test Booklet 567 33. For the population of people in the United States who are at least years of age, approximately percent voted in a recent election. A random sample of people and a random sample of people will be selected from the population. For which sample size is it more likely that greater than percent of the sample voted in the recent election? (A) They are equally likely, because the mean of the sampling distribution is the same for both sample sizes. 34. (B) It is more likely for a sample size of distribution for larger sample sizes. people, because there is more variability in the sampling (C) It is more likely for a sample size of for larger sample sizes. people, because there is less variability in the sampling distribution (D) It is more likely for a sample of size distribution for smaller sample sizes. people, because there is more variability in the sampling (E) It is more likely for a sample size of for smaller sample sizes. people, because there is less variability in the sampling distribution The mean and standard deviation of the sample data collected on continuous variable are and 0.03, respectively. The following table shows the relative frequencies of the data in the given intervals. Interval Relative Frequency 0.02 0.15 0.33 0.36 0.11 0.03 Based on the table, do the data support the use of a normal model to approximate population characteristics? (A) Yes, because the sum of the relative frequencies is 1.00. (B) Yes, because the distribution of relative frequencies is very close to the empirical rule for normal models. (C) No, because the values are negative and normal models are used for positive values. (D) No, because the distribution of relative frequencies is very far from the empirical rule for normal models. (E) Page 10 of 86 No, because the sample size and the population parameters are not known. AP Statistics Test Booklet 567 35. The normal curve shown represents the sampling distribution of a sample mean for sample size n = 25, selected at random from a population with standard deviation . Which of the following is the best estimate of the standard deviation of the population, ? (A) 3 (B) 6 (C) 15 (D) 30 (E) 36. 75 Samples G and H were selected from the same population of quantitative data and the mean of each sample was determined. The mean of sample G is equal to the mean of the population. Which of the following statements must be true? I. The mean of sample H must also be equal to the population mean. II. The mean of sample G, , is a point estimator for the mean of the population. III. The mean of sample H, , is a point estimator for the mean of the population. (A) (B) (C) (D) (E) only only only and and AP Statistics Page 11 of 86 Test Booklet 567 37. The following graphs show the sampling distributions for two different point estimators, population parameter. and , of the same Which of the following statements is true? (A) Both and are unbiased. (B) and are biased. (C) is biased, and (D) is unbiased, and (E) 38. Both is unbiased. is biased. The assessment of bias is not possible, because the sampling distributions display too much variability. The distribution of the length of employment for workers at a factory is moderately skewed to the right, with mean years and standard deviation years. The factory manager will select a random sample of employees to survey. Which of the following best describes the sampling distribution of the sample means of length of employment for ? samples of size (A) Moderately skewed to the right, with mean years and standard deviation (B) Moderately skewed to the right, with mean years and standard deviation less than (C) Moderately skewed to the right, with mean less than (D) Approximately normal, with mean less than (E) 39. Approximately normal, with mean years years years and standard deviation less than years and standard deviation years years and standard deviation less than years years In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B? Page 12 of 86 AP Statistics Test Booklet 567 (A) The centers will roughly be equal, and the variabilities will roughly be equal. 40. (B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B. (C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B. (D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B. (E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B. The graph shows the population distribution of random variable with mean Which of the following graphs is a sampling distribution of the sample mean the population? and standard deviation for samples of size AP Statistics . taken from Page 13 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 41. Suppose that 25 percent of women and 22 percent of men would answer yes to a particular question. In a simulation, a random sample of 100 women and a random sample of 100 men were selected, and the difference in sample proportions of those who answered yes, p̂women - p̂men, was calculated. The process was repeated 1,000 times. Which of the following is most likely to be a representation of the simulated sampling distribution of the difference between the two sample proportions? Page 14 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) AP Statistics Page 15 of 86 Test Booklet 567 (E) 42. In a large school district, 16 of 85 randomly selected high school seniors play a varsity sport. In the same district, 19 of 67 randomly selected high school juniors play a varsity sport. A 95 percent confidence interval for the difference between the proportion of high school seniors who play a varsity sport in the school district and high school juniors who play a varsity sport in the school district is to be calculated. What is the standard error of the difference? (A) 0.0347 (B) 0.0695 (C) 0.1362 (D) 0.9800 (E) Page 16 of 86 1.6900 AP Statistics Test Booklet 567 43. Attendance records at a large high school show that percent of students are late to school on a typical day. The students in an AP Statistics class believe the rate is higher than percent. The students took a simple random sample of students from the school and asked, “Were you late to school today?” In their sample, out of the students, or percent of the sample, said they were late to school that day. The AP Statistics students conducted a simulation with samples of students from a population where percent of students are late. The results of the simulation are shown in the dotplot. Based on the simulation and the results of the AP Statistics class’s sample, is there convincing statistical evidence that more than percent of all students at the school are late to school on a typical day? (A) Yes, because of students in their sample said they were late to school that day. (B) Yes, because about (C) No, because about (D) Yes, because about (E) 44. No, because about of the simulated sample percentages of students late to school are of the simulated sample percentages of students late to school are of the simulated sample percentages of students late to school are of the simulated sample percentages of students late to school are or more. or more. or more. or more. On any given day, the proportion of workers at a factory who are more than 5 minutes late to work is 0.11. A random sample of 20 workers will be selected. Which of the following is the best interpretation of the mean of the sampling distribution of the sample proportion of workers in the sample who are more than 5 minutes late to work for samples of size 20 ? (A) For all samples of size 20, the mean of all possible sample proportions is equal to 0.11. (B) For a randomly selected worker, the probability the worker will be more than 5 minutes late to work is 0.11. (C) For a random sample of 20 workers, the proportion of workers who are more than 20 minutes late to work will be 0.11. (D) For a random sample of 20 workers, the probability that 2.2 workers will be more than 5 minutes late to work is very high. (E) For repeated samples of size 20, the proportion of workers who are more than 5 minutes late to work varies in each sample by no more than 0.11. AP Statistics Page 17 of 86 Test Booklet 567 45. A manufacturing company uses two different machines, A and B, each of which produces a certain item part. The number of defective parts produced by each machine is about 1 percent. Suppose two independent random samples, each of size 100, are selected, where one is a sample of parts produced by machine A and the other is a sample of parts produced by machine B. Which of the following is true about the sampling distribution of the difference in the sample proportions of defective parts? (A) The mean is 0 and the distribution is approximately normal. (B) The mean is 0 and the distribution will not be approximately normal. (C) The mean is 0.01 and the distribution is approximately normal. (D) The mean is 0.01 and the distribution will not be approximately normal. (E) 46. The mean is 1 and the distribution is approximately normal. A large manufacturing company has tens of thousands of employees, and percent of the employees have completed a management training course. Suppose a simple random sample of employees is selected. Which of the following is closest to the probability that more than half of the sample will be employees who have completed the management training course? (A) (B) (C) (D) (E) 47. A fair die has its faces numbered from 1 to 6. Let random variable represent the number landing face up when the die is tossed. The probability distribution for the random variable has mean 3.5 and standard deviation 1.7078. Consider a simulation with 400 trials designed to estimate the sampling distribution of the sample mean for 5 tosses of the die. For each trial, the die is tossed 5 times, and the mean of the 5 values landing face up is recorded. The mean and standard deviation of the results of the simulation should be close to which of the following? (A) Mean 3.5 and standard deviation 1.7078 (B) Mean 3.5 and standard deviation 0.7638 (C) Mean 3.5 and standard deviation 0.0854 (D) Mean 17.5 and standard deviation 1.7078 (E) Page 18 of 86 Mean 17.5 and standard deviation 0.7638 AP Statistics Test Booklet 567 48. A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation. Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal? (A) The samples were not selected at random. (B) The sample size was not sufficiently large. (C) The population distribution was approximately normal. (D) The samples were selected without replacement. (E) 49. The sample means were less than the population mean. City officials estimate that 46 percent of all city residents are in favor of building a new city park. A random sample of 150 city residents will be selected. Suppose that 51 percent of the sample are in favor of building a new city park. Which of the following is true about the sampling distribution of the sample proportion for samples of size 150 ? (A) The distribution is not normal, and the mean is 0.46. (B) The distribution is not normal, and the mean is 0.51. (C) The distribution is not normal, and the mean is the average of 0.46 and 0.51. (D) The distribution is approximately normal, and the mean is 0.46. (E) 50. The distribution is approximately normal, and the mean is 0.51. The continuous random variable has a normal distribution with mean 7.5 and standard deviation 2.5. For which of the following is the probability equal to 0 ? (A) (B) (C) (D) (E) or AP Statistics Page 19 of 86 Test Booklet 567 51. 52. Data will be collected on the following variables. Which variable is most likely to be approximated by a normal model? (A) The distribution of the number of books read last week by middle school students, where the right tail of the distribution is longer than the left (B) The distribution of life span, in minutes, for batteries of a certain size, where most life spans cluster around the center of the distribution but with some very low and some very high life spans (C) The distribution of ages, in years, of the students at a certain college, where most students are between 18 and 22 years old, but ages greater than 22 will probably be more spread out than ages less than 18 (D) The distribution of the number of birthdays per month for the employees at a certain company, where the number of birthdays in each month is approximately equal (E) The distribution of the length of a stay, in days, in a hospital after surgery, where many patients have very short hospital stays, but some stays are quite lengthy and considered high outliers Clara recorded 50 numerical observations on a certain variable and then calculated the mean and the standard deviation for the observations. To help decide whether a normal model is appropriate, she created the following chart. In Clara’s chart, the letters the following list of counts for with a normal approximation? (A) 1, 7, 34, 7, 1 (B) 1, 10, 28, 10, 1 (C) 2, 8, 30, 8, 2 (D) 2, 4, 38, 4, 2 (E) Page 20 of 86 5, 5, 30, 5, 5 AP Statistics represent the number of observations falling in each interval. Which of , respectively, is the best indicator that the variable can be modeled Test Booklet 567 53. The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations. Which of the following is the correct ordering of the graphs from least value of n to greatest value of n ? (A) A, C, B (B) B, A, C (C) B, C, A (D) C, A, B (E) 54. C, B, A The mean number of pets owned by the population of students at a large high school is 3.2 pets per student with a standard deviation of 1.7 pets. A random sample of 16 students will be selected and the mean number of pets for the sample will be calculated. What is the mean of the sampling distribution of the sample mean for samples of size 16 ? (A) 1.7 (B) 3.2 (C) (D) (E) AP Statistics Page 21 of 86 Test Booklet 567 55. A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0.90. The population proportion of kernels that will pop for Brand S is 0.85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0.92 Brand S 200 0.89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0.03. Is the consumer group’s claim correct? (A) Yes. The mean is (B) No. The mean is . (C) No. The mean is . (D) No. The mean is . (E) 56. . No. The mean is . The distribution of time needed to complete a certain programming task is approximately normal, with mean 47 minutes and standard deviation 6 minutes. Which of the following is closest to the probability that a randomly chosen task will take less than 34 minutes or more than 60 minutes to complete? (A) 0.0151 (B) 0.0303 (C) 0.4849 (D) 0.9697 (E) 57. 0.9849 Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator? (A) A sample of size 25 will produce more variability of the estimator than a sample of size 50. (B) A sample of size 25 will produce less variability of the estimator than a sample of size 50. (C) A sample of size 25 will produce a biased estimator, but a sample size of 50 will produce an unbiased estimator. (D) A sample of size 25 will produce a more biased estimator than a sample of size 50. (E) Page 22 of 86 A sample of size 25 will produce a less biased estimator than a sample of size 50. AP Statistics Test Booklet 567 58. City R is a large city with 4 million residents, and City S is a smaller city with 0.25 million residents. Researchers believe that the proportion of City S residents who regularly ride bicycles is between 10 percent and 25 percent and the proportion of City R residents who regularly ride bicycles is between 20 percent and 50 percent. Suppose two independent random samples of residents from each city will be taken and the proportion of residents who ride bicycles is recorded. Based on the population proportions of residents who regularly ride bicycles, which of the following sample sizes is large enough to guarantee that the sampling distribution of the difference in sample proportions will be approximately normal? (A) 30 in City R and 30 in City S (B) 30 in City R and 60 in City S (C) 60 in City R and 30 in City S (D) 50 in City R and 100 in City S (E) 59. 100 in City R and 50 in City S A sample of size will be selected from a population with population proportion . Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal? (A) Both and (B) is greater than 30. (C) is greater than 0.5. (D) The mean is equal to (E) 60. are at least 10. . The variance is equal to . A certain statistic will be used as an unbiased estimator of a parameter. Let represent the sampling distribution of represent the sampling distribution of the estimator for samples of the estimator for samples of size 40, and let size 100. Which of the following must be true about ? (A) The expected value of the variability of . will be equal to the expected value of (B) The expected value of than the variability of will be greater than the expected value of . , and the variability of will be greater (C) The expected value of than the variability of will be greater than the expected value of . , and the variability of will be less , and the variability of will be equal to (D) The expected values of and will be equal, and the variability of will equal the variability of The expected values of . and will be equal, and the variability of will be greater than the variability of (E) 61. and . For a certain population of sea turtles, 18 percent are longer than 6.5 feet. A random sample of 90 sea turtles will be selected. What is the standard deviation of the sampling distribution of the sample proportion of sea turtles longer than 6.5 feet for samples of size 90 ? AP Statistics Page 23 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 62. The histogram below represents data obtained after the census of an entire population was conducted. The sampling distribution of the sample mean based on samples of size 2 for the population was simulated, and a histogram of the results was produced. Which of the following histograms is most likely the histogram of that sampling distribution? Page 24 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) AP Statistics Page 25 of 86 Test Booklet 567 (E) 63. In a recent year, the distribution of age for senators in the United States Senate was unimodal and roughly symmetric with mean years and standard deviation years. Consider a simulation with trials in which, for each trial, a random sample of senators’ ages is selected and the mean age calculated. Which of the following best describes the distribution of the (A) Approximately normal with mean years and standard deviation years (B) Approximately normal with mean years and standard deviation years (C) Approximately normal with mean years and standard deviation (D) Approximately uniform with mean years and standard deviation Approximately uniform with mean years and standard deviation (E) 64. sample mean ages? years years years For which of the following is the shape of the sampling distribution of the sample mean approximately normal? I. A random sample of size 5 from a population that is approximately normal II. A random sample of size 10 from a population that is strongly skewed to the right III. A random sample of size 60 from a population that is strongly skewed to the left (A) only (B) 65. only (C) and (D) and (E) , only only , and Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded. Are the sample sizes large enough to assume that the sampling distribution of the difference in sample proportions is approximately normal? Page 26 of 86 AP Statistics Test Booklet 567 (A) Yes. Both sample sizes are large enough. (B) No. The sample size for drug X is large enough, but the sample size for drug Y is not. (C) No. The sample size for drug Y is large enough, but the sample size for drug X is not. (D) No. Neither sample size is large enough. (E) There is not enough information provided to determine whether the sampling distribution is approximately normal. 66. A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? (A) Bimodal (B) Uniform (C) Approximately normal (D) Strongly skewed to the left (E) 67. Strongly skewed to the right The manager of a symphony in a large city wants to investigate music preferences for adults and students in the city. Let represent the population proportion of adults who live in the city who prefer pop music. Let represent the population proportion of students who live in the city who prefer pop music. Random samples of 200 adults from the city and 200 students from the city will be selected. Which of the following is the best interpretation of ? (A) The difference between the population proportion of adults who prefer pop music and the population proportion of students who prefer pop music is approximately 0.022. (B) The difference between the population proportion of adults who prefer pop music and the population proportion of students who prefer pop music is 0. (C) For all random samples of 200 adults from the city and 200 students from the city, the difference between the sample proportion of adults who prefer pop music and the sample proportion of students who prefer pop music will be 0.022. For all random samples of 200 adults from the city and 200 students from the city, the difference between the (D) sample proportion of adults who prefer pop music and the sample proportion of students who prefer pop music will be 0. (E) For all random samples of 200 adults from the city and 200 students from the city, the sample proportion of adults who prefer pop music will be greater than the sample proportion of students who prefer pop music in about 2.2% of samples. AP Statistics Page 27 of 86 Test Booklet 567 68. A large school district held a district-wide track meet for all high school students. For the 2-mile run, the population of female students participating had a mean running time of 8.8 minutes with standard deviation of 3.3 minutes, and the population of male students participating had a mean running time 7.3 minutes with standard deviation of 2.9 minutes. Suppose 8 female students and 8 male students who participated in the 2-mile run are selected at random from each population. Let represent the sample mean running time for the female students, and let represent the sample mean running time for the male students. What are the mean and standard deviation of the sampling distribution of the difference in sample means ? (A) The mean is 0.4, and the standard deviation is (B) The mean is 0.4, and the standard deviation is . (C) The mean is 1.5, and the standard deviation is . (D) The mean is 1.5, and the standard deviation is (E) 69. . The mean is 1.5, and the standard deviation is . . A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution? (A) 234 grams (B) 240 grams (C) 243 grams (D) 246 grams (E) 70. 248 grams Cheryl practices hitting a softball in an indoor stadium by using both an aluminum bat and a composite bat made of carbon fiber and graphite. She records the distance traveled by the ball for each hit. Let represent the average distance traveled by balls hit with the aluminum bat, and let represent the average distance traveled by balls hit with the composite bat. Assume Cheryl’s batting practice hits are independent. Which of the following conditions are sufficient to model the sampling distribution of distribution? I. There are at least 30 recorded distances traveled for each type of bat. II. The distribution of distance traveled by the ball is approximately normal for each bat. III. The total number of distances traveled is at least 60 for the two bats combined. (A) (B) (C) (D) (E) Page 28 of 86 only only only and only and only AP Statistics with a normal Test Booklet 567 71. For a population of leghorn chickens, the mean number of eggs laid per chicken is 0.70 with standard deviation 0.20 egg. For a population of Sussex chickens, the mean number of eggs laid per chicken is 0.50 with standard deviation 0.10 egg. Two independent random samples of chickens were taken from the populations. The following table shows the sample statistics. Leghorn 36 0.75 0.30 Sussex 36 0.45 0.12 Mike claims that for all samples of size 36 from the population of leghorn chickens and all samples of size 36 from the population of Sussex chickens, the mean of all possible differences in sample means (leghorn minus Sussex) is 0.30 eggs per chicken. Is Mike’s claim correct? (A) Yes. The mean is (B) No. The mean is egg per chicken. (C) No. The mean is egg per chicken. (D) No. The mean is egg per chicken. (E) 72. egg per chicken. No. The mean is eggs per chicken. Two coins, A and B, each have a side for heads and a side for tails. When coin A is tossed, the probability it will land tails-side up is 0.5. When coin B is tossed, the probability it will land tails-side up is 0.8. Both coins will be represent the proportion of times coin A lands tails-side up, and let represent the tossed 20 times. Let proportion of times coin B lands tails-side up. Is the number of tosses for each coin enough for the sampling distribution of the difference in sample proportions to be approximately normal? (A) Yes, 20 tosses for each coin is enough. (B) No, 20 tosses for coin A is enough, but 20 tosses for coin B is not enough. (C) No, 20 tosses for coin A is not enough, but 20 tosses for coin B is enough. (D) No, 20 tosses is not enough for either coin. (E) 73. There is not enough information given to determine if 20 tosses is enough. The distribution of age for players of a certain professional sport is strongly skewed to the right with mean 26.8 years and standard deviation 4.2 years. Consider a random sample of 4 players and a different random sample of 50 players from the population. Which of the following statements is true about the sampling distributions of the sample mean ages for samples of size 4 and samples of size 50 ? AP Statistics Page 29 of 86 Test Booklet 567 (A) Both will be skewed to the right, and the mean for size 50 will be closer to 26.8 than the mean for size 4. 74. (B) Both will be skewed to the right, and the standard deviation for size 50 will be closer to 4.2 than the standard deviation for size 4. (C) Both will be approximately normal, and the mean for size 50 will be closer to 26.8 than the mean for size 4. (D) Only the sampling distribution for size 4 will be approximately normal, and the standard deviation for both will be 4.2. (E) Only the sampling distribution for size 50 will be approximately normal, and the mean for both will be 26.8. A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of 50 trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described? Page 30 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) AP Statistics Page 31 of 86 Test Booklet 567 75. For a particular video game, Ariana’s mean number of points earned per game is , and the standard deviation is . Suppose that she plays games in one evening, and her goal is to obtain a mean score of at least for the games. How many standard deviations above is her goal? (A) (B) (C) (D) (E) 76. The distribution of ocean wave height at a certain California beach is approximately normal with mean 7.2 feet. The distribution of ocean wave height at a certain Florida beach is approximately normal with mean 6.6 feet. Six waves from each beach will be selected at random and the heights will be recorded. Let represent the sample mean height of the 6 California waves, and let represent the sample mean height of the 6 Florida waves. Which of the following is the best interpretation of ? (A) The probability that the heights for all 6 California waves will exceed the heights for all 6 Florida waves by more than 0.55 feet is 0.5. (B) The probability that the heights for all 6 California waves will exceed the heights for all 6 Florida waves by more than 0.5 feet is 0.55. (C) The probability of observing a difference (California minus Florida) greater than 0.5 feet between the mean height of 6 California waves and the mean height of 6 Florida waves is 0.55. (D) The probability of observing a difference greater than 0.5 feet between the height of one wave in California and the height of one wave in Florida is 0.55. (E) The probability of observing a difference greater than 0.55 feet between the height of one wave in California and the height of one wave in Florida is 0.5. Page 32 of 86 AP Statistics Test Booklet 567 77. Researchers are studying two populations of wild horses living in the western regions of a country. In a random sample of 32 horses taken from the first population, the mean age of the sample was 21 years. In a random sample of 41 horses from the second population, the mean age of the sample was 19 years. Is the sampling distribution of the difference in sample mean ages approximately normal? (A) Yes, because the two populations of wild horses can be modeled by a normal distribution. (B) Yes, because the samples were selected at random. (C) Yes, because the sample sizes are both greater than 30. (D) No, because the populations are not normal. (E) 78. No, because the difference in sample mean ages was not 0. At a large corporation, 6,000 employees from department A and 4,000 employees from department B are attending a training session. A random sample of 500 employees attending the session will be selected. Consider two sampling methods: with replacement and without replacement. How will the methods affect the standard deviations of the sampling distribution of the sample proportion of employees from department B? (A) The standard deviations will be equal from either method. (B) Sampling without replacement will result in a standard deviation less than but close to (C) Sampling without replacement will result in a standard deviation greater than but close to (D) Sampling with replacement will result in a standard deviation less than but close to (E) 79. Sampling with replacement will result in a standard deviation greater than but close to . . . . A reading specialist wanted to estimate the mean word length, in number of letters, for an elementary school history textbook. The specialist took repeated random samples of size 100 words and estimated the mean and standard deviation of the sampling distribution to be 4.9 letters and 0.15 letter, respectively. Based on the estimates for the sampling distribution, which of the following provides the best estimates of the population parameters? (A) Mean 4.9 letters and standard deviation 0.015 letter (B) Mean 4.9 letters and standard deviation 0.15 letter (C) Mean 4.9 letters and standard deviation 1.5 letters (D) Mean 0.49 letter and standard deviation 0.15 letter (E) 80. Mean 49 letters and standard deviation 15 letters The statistic is used as an estimator for which of the following? AP Statistics Page 33 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 81. At a large corporation, the distribution of years of employment for the employees has mean 20.6 years and standard deviation 5.3 years. A random sample of 100 employees was selected and surveyed about employee satisfaction. The sample of employees had a mean 20.3 years and standard deviation 6.1 years. Remy claims that the mean of the sampling distribution of the sample mean for samples of size 100 is 20.6 years. Is Remy’s claim correct? (A) No. The mean of the sampling distribution is 20.3 years. (B) No. The mean of the sampling distribution is 20.3 employees. (C) No. The mean of the sampling distribution is 5.3 years. (D) No. The mean of the sampling distribution is 20.6 employees. (E) 82. Yes. The mean of the sampling distribution is 20.6 years. A 90 percent confidence interval is to be created to estimate the proportion of television viewers in a certain area who favor moving the broadcast of the late weeknight news to an hour earlier than it is currently. Initially, the confidence interval will be created using a simple random sample of 9,000 viewers in the area. Assuming that the sample proportion does not change, what would be the relationship between the width of the original confidence interval and the width of a second 90 percent confidence interval that is created based on a sample of only 1,000 viewers in the area? (A) The second confidence interval would be 9 times as wide as the original confidence interval. (B) The second confidence interval would be 3 times as wide as the original confidence interval. (C) The width of the second confidence interval would be equal to the width of the original confidence interval. (D) The second confidence interval would be 1/3 as wide as the original confidence interval. (E) 83. The second confidence interval would be 1/9 as wide as the original confidence interval. A 95 percent confidence interval of the form p̂ ± E will be used to obtain an estimate for an unknown population proportion p. If p̂ is the sample proportion and E is the margin of error, which of the following is the smallest sample size that will guarantee a margin of error of at most 0.08? (A) 25 (B) 100 (C) 175 (D) 250 (E) Page 34 of 86 625 AP Statistics Test Booklet 567 84. A 99 percent one-sample z-interval for a proportion will be created from the point estimate obtained from each of two random samples selected from the same population: sample R and sample S. Let R represent a random sample of size 1,000, and let S represent a random sample of size 4,000. If the point estimate obtained from R is equal to the point estimate obtained from S, which of the following must be true about the respective margins of error constructed from those samples? (A) The margin of error for S will be 4 times the margin of error for R. (B) The margin of error for S will be 2 times the margin of error for R. (C) The margin of error for S will be equal to the margin of error for R. (D) The margin of error for R will be 4 times the margin of error for S. (E) 85. The margin of error for R will be 2 times the margin of error for S. A candy company claims that 10 percent of its candies are blue. A random sample of 200 of these candies is taken, and 16 are found to be blue. Which of the following tests would be most appropriate for establishing whether the candy company needs to change its claim? (A) Matched pairs t-test (B) One-sample proportion z-test (C) Two-sample t-test (D) Two-sample proportion z-test (E) 86. Chi-square test of association A commercial for a breakfast cereal is shown during a certain television program. The manufacturer of the cereal wants to estimate the percent of television viewers who watch the program. The manufacturer wants the estimate to have a margin of error of at most 0.02 at a level of 95 percent confidence. Of the following, which is the smallest sample size that will satisfy the manufacturer’s requirements? (A) 40 (B) 50 (C) 100 (D) 1,700 (E) 87. 2,500 A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with the specifications, the company’s quality control manager selected a random sample of 1,000 packages produced in one week and found 40 packages, or 4 percent, to be underweight. Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of that more than 3 percent of all the packages produced in one week are underweight? (A) Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03. (B) Yes, because the p-value of 0.032 is less than the significance level of 0.05. (C) Yes, because the p-value of 0.064 is greater than the significance level of 0.05. (D) No, because the p-value of 0.032 is less than the significance level of 0.05. (E) No, because the p-value of 0.064 is greater than the significance level of 0.05. AP Statistics Page 35 of 86 Test Booklet 567 88. 89. A large clinical trial was designed to determine whether a certain vitamin improves the general health of adults. The investigators first identified 85 variables that measure various aspects of the general health of adults. Because each adult in the clinical trial was to serve as his or her own control, the 85 variables were measured for each adult, both before taking the vitamin and after taking the vitamin for three months. The investigators then performed 85 matched-pair t-tests, one for each variable. They found statistically significant results at the 0.05 level in 2 of the variables, both in the direction of improved general health. Which of the following should the investigators conclude? (A) There is evidence that the vitamin improves the health of adults because 2 of the 85 tests were statistically significant. (B) There is evidence that the vitamin improves the health of adults because in clinical trials investigators typically underestimate the proportion of the population that is helped by a vitamin. (C) There is insufficient evidence that the vitamin improves the health of adults because at the 0.05 significance level, one could easily get statistically significant results in 2 out of 85 tests just due to chance variability. (D) There is insufficient evidence that the vitamin improves the health of adults because the sample size of 85 is not large enough to draw a conclusion. (E) No conclusion can be drawn because an even number of variables is needed for a matched-pairs design. A large-sample 98 percent confidence interval for the proportion of hotel reservations that are canceled on the intended arrival day is (0.048, 0.112). What is the point estimate for the proportion of hotel reservations that are canceled on the intended arrival day from which this interval was constructed? (A) 0.032 (B) 0.064 (C) 0.080 (D) 0.160 (E) 90. It cannot be determined from the information given. A marketing company wants to estimate the proportion of consumers in a certain region of the country who would react favorably to a new marketing campaign. Further, the company wants the estimate to have a margin of error of no more than 5 percent with 90 percent confidence. Of the following, which is closest to the minimum number of consumers needed to obtain the estimate with the desired precision? (A) 136 (B) 271 (C) 385 (D) 542 (E) 91. 769 A national health study reported that the proportion of students with elevated blood pressure is 0.15. The principal of a local high school believes that the proportion of students in the school with elevated blood pressure is greater than 0.15. If a large random sample is used, which of the following is the most appropriate test to investigate the principal’s belief? Page 36 of 86 AP Statistics Test Booklet 567 (A) A z-test for a proportion (B) A z-test for a difference between two proportions (C) A chi-square test for homogeneity of proportions (D) A t-test for a mean (E) 92. A matched-pairs t-test An environmental group wanted to estimate the proportion of fresh produce sales identified as organic in a local grocery store. In the winter, the group obtained a random sample of sales from the store and used the data to construct the 95 percent z-interval for a proportion (0.087, 0.133 ). Six months later in the summer, the group obtained a second random sample of sales from the store. The second sample was the same size as the first, and the proportion of sales identified as organic was 0.4. How does the 95 percent z-interval for a proportion constructed from the summer sample compare to the winter interval? (A) The summer interval is wider and has a lesser point estimate. (B) The summer interval is wider and has a greater point estimate. (C) The summer interval is narrower and has a lesser point estimate. (D) The summer interval is narrower and has a greater point estimate. (E) 93. The summer interval is the same width and has a greater point estimate. A news organization conducted a survey about preferred methods for obtaining the news. A random sample of 1,605 adults living in a certain state was selected, and 16.2 percent of the adults in the sample reported that television was their preferred method. Which of the following is an appropriate margin of error for a 90 percent confidence interval to estimate the population proportion of all adults living in the state who would report that television is their preferred method for obtaining the news? (A) (B) (C) (D) (E) 94. A newspaper poll found that 52 percent of the respondents in a large random sample of likely voters in a district intend to vote for candidate Smith rather than the opponent. A 95 percent confidence interval for the population proportion was computed to be 0.52 ± 0.04. Based on the confidence interval, which of the following should the newspaper report to its readers? AP Statistics Page 37 of 86 Test Booklet 567 (A) Smith will win because a majority of voters are in favor of Smith. (B) There is a 95% chance that Smith will win. (C) The poll predicts Smith will win, but there is a 5% chance that the prediction is incorrect due to sampling error. (D) With 95% confidence, there is convincing evidence that Smith will win. (E) 95. No prediction about who will win can be made with 95% confidence. An experimenter conducted a two-tailed hypothesis test on a set of data and obtained a p-value of 0.44. If the experimenter had conducted a one-tailed test on the same set of data, which of the following is true about the possible p-value(s) that the experimenter could have obtained? (A) The only possible p-value is 0.22. (B) The only possible p-value is 0.44. (C) The only possible p-value is 0.88. (D) The possible p-values are 0.22 and 0.78. (E) 96. 97. The possible p-values are 0.22 and 0.88. A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation of the 95 percent confidence level? (A) With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the United States who are optimistic about the economy is correct. (B) We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy. (C) We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of the United States who are optimistic about the economy. (D) Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from samples of the same size of 1,200. (E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sample proportion of citizens of the United States who are optimistic about the economy. A polling agency reported that 66 percent of adults living in the United States were satisfied with their health care plans. The estimate was taken from a random sample of 1,542 adults living in the United States, and the 95 percent confidence interval for the population proportion was calculated as (0.636, 0.684). Which of the following statements is a correct interpretation of the 95 percent confidence level? Page 38 of 86 AP Statistics Test Booklet 567 98. (A) The probability is 0.95 that the percent of adults living in the United States who are satisfied with their health care plans is between 63.6% and 68.4%. (B) Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults living in the United States who are satisfied with their health care plans. (C) Approximately 95% of random samples of the same size from the population will result in a confidence interval that includes the proportion of all adults in the sample who are satisfied with their health care plans. (D) Approximately 95% of all random samples of adults living in the United States will indicate that between 63.6% and 68.4% of the adults are satisfied with their health care plans. (E) Approximately 95% of all random samples of adults living in the United States will result in a sample proportion of 0.66 adults living in the United States who are satisfied with their health care plans. A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. The table shows the responses by level of support. Based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal? (A) (B) (C) (D) (E) 99. A random sample of 300 students is selected from a large group of students who use a computer-equipped classroom on a regular basis. Occasionally, students leave their USB drive in a computer. Of the 300 students questioned, 180 said that they write their name on their USB drive. Which of the following is a 98 percent confidence interval for the proportion of all students using the classroom who write their name on their USB drive? AP Statistics Page 39 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 100. A random sample of 432 voters revealed that 100 are in favor of a certain bond issue. A 95 percent confidence interval for the proportion of the population of voters who are in favor of the bond issue is (A) (B) (C) (D) (E) 101. A recent survey estimated that 19 percent of all people living in a certain region regularly use sunscreen when going outdoors. The margin of error for the estimate was 1 percentage point. Based on the estimate and the margin of error, which of the following is an appropriate conclusion? (A) Approximately 1% of all the people living in the region were surveyed. (B) Between 18% and 20% of all the people living in the region were surveyed. (C) All possible samples of the same size will result in between 18% and 20% of those surveyed indicating they regularly use sunscreen. (D) The probability is 0.01 that a person living in the region will use sunscreen when going outdoors. (E) It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%. 102. A representative of a car manufacturer in the United States made the following claim in a news report. Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today. A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago? Page 40 of 86 AP Statistics Test Booklet 567 (A) Yes, because 0.56 > 0.53. (B) Yes, because a reasonable interval for the proportion is 0.56 ± 0.283. (C) Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05. (D) No, because 0.283 < 0.53. (E) No, because 0.283 > 0.05. 103. A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher? (A) H0: p = 0.5 and Ha: p > 0.5 (B) H0: p = 0.5 and Ha: p ≠ 0.5 (C) H0: p = 0.5 and Ha: p < 0.5 (D) H0: p > 0.5 and Ha: p ≠ 0.5 (E) H0: p > 0.5 and Ha: p = 0.5 104. A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample -interval been met? (A) Yes, all conditions for inference have been met. (B) No, because the sample size is not large enough to satisfy the conditions for normality. (C) No, because the sample was not selected at random. (D) No, because the sample size is not less than 10 percent of the population size. (E) No, because the sample is not representative of the population. 105. A school administrator is interested in estimating the proportion of students in the district who participate in community service activities. From a random sample of 100 students in the district, the administrator will construct a 99 percent confidence interval for the proportion of all district students who participate in community service activities. Which of the following statements must be true? (A) The population proportion will be in the confidence interval. (B) The probability that the confidence interval will include the population proportion is 0.99. (C) The probability that the confidence interval will include the sample proportion is 0.99. (D) The population proportion and the sample proportion will be equal. (E) The probability that the population proportion and the sample proportion will be equal is 0.99. 106. A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. Which of the following is the test statistic for the appropriate test? AP Statistics Page 41 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 107. A survey was conducted to determine what percentage of college seniors would have chosen to attend a different college if they had known then what they know now. In a random sample of 100 seniors, 34 percent indicated that they would have attended a different college. A 90 percent confidence interval for the percentage of all seniors who would have attended a different college is (A) 24.7% to 43.3% (B) 25.8% to 42.2% (C) 26.2% to 41.8% (D) 30.6% to 37.4% (E) 31.2% to 36.8% 108. Based on a survey of a random sample of 900 adults in the United States, a journalist reports that 60 percent of adults in the United States are in favor of increasing the minimum hourly wage. If the reported percent has a margin of error of 2.7 percentage points, which of the following is closest to the level of confidence? (A) 80.0% (B) 90.0% (C) 95.0% (D) 95.5% (E) 99.0% 109. In a population of bats living in a certain region, 30 percent have a wingspan greater than 10 inches. In a random sample of 80 bats living outside of the region, 20 had a wingspan greater than 10 inches. Consider a one-sample -test to investigate whether there is evidence that the proportion of bats with a wingspan greater than 10 inches living outside the region is different from that of the bats living in the region. Which of the following is the correct test statistic? Page 42 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) 110. A company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that versus at the arrived with broken glass. The manufacturer tested the hypotheses significance level of The test yielded a -value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion? (A) The -value is greater than , and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. (B) The -value is greater than , and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. (C) The -value is greater than , and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. (D) The -value is less than , and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. (E) The -value is less than , and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08. 111. From a random sample of potential voters in an upcoming election, 47% indicated they intended to vote for Candidate R. A 95 percent confidence interval was constructed from the sample, and the margin of error for the estimate was 5%. Which of the following is the best interpretation of the interval? (A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%. (B) We are 95% confident that the proportion who intend to vote for Candidate R from the population is between 42% and 52%. (C) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is 47%. (D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47%. (E) We are confident that 95% of the population intend to vote for Candidate R. AP Statistics Page 43 of 86 Test Booklet 567 Each voter from a random sample of registered voters was asked their impression of two candidates running for the same national office. The table summarizes the responses. 112. Candidate A Candidate B Favorable Unfavorable No opinion Have not heard of Which of the following is the most appropriate method to use to estimate the proportion of all registered voters who have a favorable impression of Candidate A? (A) A one-sample -interval for estimating a sample proportion (B) A one-sample -interval for estimating a population proportion (C) A matched-pairs -interval for estimating a mean difference (D) A two-sample -interval for estimating a difference between sample proportions (E) A two-sample -interval for estimating a difference between population proportions 113. Courtney has constructed a cricket out of paper and rubber bands. According to the instructions for making the cricket, when it jumps it will land on its feet half of the time and on its back the other half of the time. In the first 50 jumps, Courtney's cricket landed on its feet 35 times. In the next 10 jumps, it landed on its feet only twice. Based on this experience, Courtney can conclude that (A) the cricket was due to land on its feet less than half the time during the final 10 jumps, since it had landed too often on its feet during the first 50 jumps (B) a confidence interval for estimating the cricket's true probability of landing on its feet is wider after the final 10 jumps than it was before the final 10 jumps (C) a confidence interval for estimating the cricket's true probability of landing on its feet after the final 10 jumps is exactly the same as it was before the final 10 jumps (D) a confidence interval for estimating the cricket's true probability of landing on its feet is more narrow after the final 10 jumps than it was before the final 10 jumps (E) a confidence interval for estimating the cricket's true probability of landing on its feet based on the initial 50 jumps does not include 0.2, so there must be a defect in the cricket's construction to account for the poor showing in the final 10 jumps versus . The sample mean was 114. A researcher conducted a -test of the hypotheses and the -value for the test was . What would the -value have been if the researcher had used as the alternative hypothesis? Page 44 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) 115. A random sample of residents in city J were surveyed about whether they supported raising taxes to increase bus service for the city. From the results, a 95 percent confidence interval was constructed to estimate the proportion of people in the city who support the increase. The interval was . Based on the confidence interval, which of the following claims is supported? (A) More than 90 percent of the residents support the increase. (B) More than 60 percent of the residents support the increase. (C) More than 40 percent of the residents support the increase. (D) Fewer than 10 percent of the residents support the increase. (E) Fewer than 25 percent of the residents support the increase. 116. A random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as . Which of the following is a correct interpretation of the interval? (A) We are 95 percent confident that any sample of 1,175 people will produce a sample proportion between 0.146 and 0.214. (B) We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214. (C) We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214. (D) The probability that 95 percent of all people in the country who think climate change is a problem is between 0.146 and 0.214. (E) The probability is 0.95 that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214. 117. A city planner wants to estimate the proportion of city residents who commute to work by subway each day. A random sample of 30 city residents was selected, and 28 of those selected indicated that they rode the subway to work. Is it appropriate to assume that the sampling distribution of the sample proportion is approximately normal? (A) No, because the size of the population is not known. (B) No, because the sample is not large enough to satisfy the normality conditions. (C) Yes, because the sample is large enough to satisfy the normality conditions. (D) Yes, because the sample was selected at random. (E) Yes, because sampling distributions of proportions are modeled with a normal model. AP Statistics Page 45 of 86 Test Booklet 567 employees. The director of human resources at the company selects of the 118. A technology company has employees at random, without replacement, and asks them to fill out an anonymous survey asking whether they plan to attend the company’s holiday party. The proportion of employees in the sample who plan to attend the party is . Based on this proportion, the director calculates a percent confidence interval for the proportion of all . employees who plan to attend the holiday party as Which of the following is true concerning whether it is appropriate to use the confidence interval to estimate the proportion of all employees who plan to attend the holiday party? (A) The confidence interval is appropriate to use because the employees were randomly selected. (B) The confidence interval is not appropriate to use because one of the values than . (C) The confidence interval is not appropriate to use because at the company. (D) The confidence interval is appropriate to use because (E) The confidence interval is appropriate to use because and employees is more than and are greater than is less than of all employees . . 119. The management team of a company with 10,000 employees is considering installing charging stations for electric cars in the company parking lots. In a random sample of 500 employees, 15 reported owning an electric car. Which of the following is a 99 percent confidence interval for the proportion of all employees at the company who own an electric car? (A) (B) (C) (D) (E) 120. The p-value for a one-sided t-test is 0.10. If the test had been two-sided, what would the p-value have been? Page 46 of 86 AP Statistics Test Booklet 567 (A) 0.05 (B) 0.20 (C) 0.90 (D) 0.95 (E) It depends on the direction of the alternative hypothesis. 121. In 2009 a survey of Internet usage found that 79 percent of adults age 18 years and older in the United States use the Internet. A broadband company believes that the percent is greater now than it was in 2009 and will conduct a survey. The company plans to construct a 98 percent confidence interval to estimate the current percent and wants the margin of error to be no more than 2.5 percentage points. Assuming that at least 79 percent of adults use the Internet, which of the following should be used to find the sample size (n) needed? (A) (B) (C) (D) (E) percent of adults who were asked to describe their day responded that they 122. A research organization reported that were having a good day rather than a typical day or a bad day. To investigate whether the percent would be different for high school students, high school students were randomly selected. When asked to describe their students reported that they were having a good day rather than a typical day or a bad day. Do the data day, provide convincing statistical evidence that the proportion of all high school students who would respond that they were having a good day is different from ? (A) No, because the -value is less than any reasonable significance level. (B) No, because the -value is greater than any reasonable significance level. (C) Yes, because the -value is less than any reasonable significance level. (D) Yes, because the -value is greater than any reasonable significance level. (E) Yes, because the expected value of the number of students who will report having a good day is . , not 123. In order to make statistical inferences when testing a population proportion , which of the following conditions verify that inference procedures are appropriate? I. The data are collected using a random sample or random assignment. II. The sample size is less than 10 percent of the population size. III. and for sample size and hypothesized proportion . AP Statistics Page 47 of 86 Test Booklet 567 (A) only (B) only only (C) (D) (E) and , only , and 124. Jessica wanted to determine if the proportion of males for a certain species of laboratory animal is less than 0.5. She was given access to appropriate records that contained information on 12,000 live births for the species. To construct a 95 percent confidence interval, she selected a simple random sample of 100 births from the records and found that 31 births were male. Based on the study, which of the following expressions is an approximate 95 percent confidence interval estimate for p, the proportion of males in the 12,000 live births? (A) (B) (C) (D) (E) adults in the United States, it was found that percent own an e-reader. Which 125. From a random sample of percent confidence interval to estimate the proportion of all adults in the of the following is the appropriate United States who own an e-reader? (A) (B) (C) (D) (E) Page 48 of 86 AP Statistics Test Booklet 567 126. Dan selected a random sample of 100 students from the 1,200 at his school to investigate preferences for making up school days lost due to emergency closings. The results are shown in the table below. Dan incorrectly performed a large sample test of the difference in two proportions using 58/100 and 42/100 and calculated a p-value of 0.02. Consequently, he concluded that there was a significant difference in preference for the two options. Which of the following best describes his error in the analysis of these data? (A) No statistical test was necessary because 0.58 is clearly larger than 0.42. (B) The results of the test were invalid because less than 10% of the population was sampled. (C) Dan performed a two-tailed test and should have performed a one-tailed test. (D) A one-sample test for a proportion should have been performed because only one sample was used. (E) More options should have been included, and a chi-square test should have been performed. 127. The manager of a restaurant plans to survey a random sample of customers to estimate the proportion of customers who would return within a week if given a coupon for a free dessert to use on their next visit. A similar coupon was given last year, and percent of the customers who were given the coupon returned within a week. The manager will use the observed proportion from last year as a preliminary estimate of the population proportion and wants the margin of error to be at most at a percent level of confidence. Of the following, which is the least number of customers who should be surveyed such that the estimate of the percent confidence interval will be no greater than ? margin of error of the (A) (B) (C) (D) (E) 128. Elly and Drew work together to collect data to estimate the percentage of their classmates who own a particular brand of shoe. Using the same data, Elly will construct a 90 percent confidence interval and Drew will construct a 99 percent confidence interval. Which of the following statements is true? (A) The midpoint of Elly’s interval will be greater than the midpoint of Drew’s interval. (B) The midpoint of Elly’s interval will be less than the midpoint of Drew’s interval. (C) The width of Elly’s interval will be greater than the width of Drew’s interval. (D) The width of Elly’s interval will be less than the width of Drew’s interval. (E) The width of Elly’s interval will be equal to the width of Drew’s interval. AP Statistics Page 49 of 86 Test Booklet 567 129. For a school fund-raiser, 600 raffle tickets were sold by students at the school, of which 88 were sold by one student, Audrey. Of the 600 tickets sold, 30 were randomly selected to receive prizes, and 7 of the 30 tickets selected were tickets sold by Audrey. To investigate how likely it was by chance alone that at least 7 of the 30 selected tickets could have been sold by Audrey, students in a statistics class ran a simulation. One trial of the simulation is described by the following steps. Step 1: From 600 chips, assign 88 red and the rest blue. Step 2: Select 30 chips at random without replacement. Step 3: Record the number of red chips in the selection of 30. The results of 1,000 trials of the simulation are shown in the histogram. Based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of Audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone? (A) Yes, because the distribution of the trials in the simulation is skewed to the right. (B) Yes, because the number in the histogram with the greatest frequency is 4, not 7. (C) Yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. (D) No, because the simulation suggests that it is likely that Audrey could sell anywhere from 0 to 11 of the selected tickets. (E) No, because the simulation suggests that Audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time. 130. The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample -test for a population proportion ? Page 50 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) 131. A one-sample -test for a population proportion will be conducted using a simple random sample selected without replacement from a population. Which of the following is a check for independence? (A) and for sample size and population proportion (B) Each sample proportion value is less than or equal to 0.5. (C) The sample size is more than 10 times the population size. . (D) The population size is more than 10 times the sample size. (E) The population distribution is approximately normal. 132. On the day before an election in a large city, each person in a random sample of 1,000 likely voters is asked which candidate he or she plans to vote for. Of the people in the sample, 55 percent say they will vote for candidate Taylor. A margin of error of 3 percentage points is calculated. Which of the following statements is appropriate? The proportion of all likely voters who plan to vote for candidate Taylor must be the same as the proportion (A) of voters in the sample who plan to vote for candidate Taylor (55 percent), because the data were collected from a random sample. (B) The sample proportion minus the margin of error is greater than 0.50, which provides evidence that more than half of all likely voters plan to vote for candidate Taylor. (C) It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because the 1,000 likely voters in the sample represent only a small fraction of all likely voters in a large city. (D) It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is not an experiment. (E) It is not possible to draw any conclusion about the proportion of all likely voters who plan to vote for candidate Taylor because this is a random sample and not a census. 133. After a tropical storm in a certain state, news reports indicated that 19 percent of households in the state lost power during the storm. A state engineer believes that estimate is too low. The engineer will collect data to perform a hypothesis test on the proportion of all households without power. Which of the following are the appropriate hypotheses for such a test? AP Statistics Page 51 of 86 Test Booklet 567 (A) (B) (C) (D) (E) percent of cars registered in had a manual transmission. An automotive researcher 134. A study reported that collected data on cars registered in to investigate whether the proportion of registered cars with a manual . The researcher took a random sample of cars registered in and found transmission is less than of the cars had a manual transmission. After ensuring the conditions for inference were met, the researcher conducted an appropriate hypothesis test and . At the percent level of significance, which of the following conclusions should be calculated a -value of made? (A) The null hypothesis should be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in is less than . (B) The null hypothesis should be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in is less than . (C) The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in is not less than . (D) The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in is equal to . (E) The null hypothesis should not be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in is less than . 135. Consider a 90 percent confidence interval to estimate a population proportion that is constructed from a sample proportion of 66 percent. If the width of the interval is 10 percent, what is the margin of error? (A) 2.5 percent (B) 5 percent (C) 10 percent (D) 20 percent (E) 45 percent 136. USA Today reported that speed skater Bonnie Blair had "won the USA's heart," according to a USA Today/CNN/ Gallup poll conducted on the final Thursday of the 1994 Winter Olympics. When asked who was the hero of the Olympics, 65 percent of the respondents chose Blair, who won five gold medals. The poll of 615 adults, done by telephone, had a margin of error of 4 percent. Which of the following statements best describes what is meant by the 4 percent margin of error? Page 52 of 86 AP Statistics Test Booklet 567 (A) About 4 percent of adults were expected to change their minds between the time of the poll and its publication in USA Today. (B) About 4 percent of adults did not have telephones. (C) About 4 percent of the 615 adults polled refused to answer. (D) Not all of the 615 adults knew anything about the Olympics. (E) The difference between the sample percentage and the population percentage is likely to be less than 4 percent. 137. The manager of a magazine wants to estimate the percent of magazine subscribers who approve of a new cover format. To gather data, the manager will select a random sample of subscribers. Which of the following is the most appropriate interval for the manager to use for such an estimate? (A) A two-sample -interval for a difference between sample proportions (B) A two-sample -interval for a difference between population proportions (C) A one-sample -interval for a sample proportion (D) A one-sample -interval for a population proportion (E) A one-sample -interval for a difference between population proportions 138. The superintendent of a large school district wants to estimate the percent of district residents who support the building of a new middle school. To gather data, the superintendent will select a random sample of district residents. Which of the following is the most appropriate method for creating such an estimate? (A) A one-sample -interval for a sample proportion (B) A two-sample -interval for a difference between population proportions (C) A two-sample -interval for a population proportion (D) A one-sample -interval for a difference between population proportions (E) A one-sample -interval for a population proportion 139. A random sample of 80 people was selected, and 22 of the selected people indicated that it would be a good idea to eliminate the penny from circulation. What is the 99 percent confidence interval constructed from the sample proportion ? (A) (B) (C) (D) (E) AP Statistics Page 53 of 86 Test Booklet 567 140. Based on findings from a recent study on women’s health, researchers created a 90 percent confidence interval of to estimate the percent of all women who do not find time to focus on their own health. Based on the confidence interval, which of the following claims is not supported? (A) Less than half of all women do not find time to focus on their own health. (B) More than 40 percent of all women do not find time to focus on their own health. (C) Approximately 45 percent of all women do not find time to focus on their own health. (D) More than 45 percent of all women do not find time to focus on their own health. (E) More than 25 percent of all women do not find time to focus on their own health. 141. Consider a population with population proportion , and a sample from the population with sample proportion . Which of the following describes the purpose of the one-sample -test? (A) To estimate the value of (B) To estimate the value of (C) To estimate a margin of error for (D) To estimate the probability of observing a value as extreme as given To estimate the probability of observing a value as extreme as given (E) 142. Approximately 38 percent of people living in Region W have the blood type O positive. A random sample of 100 people from Region X revealed that 35 people in the sample had the blood type O positive. Consider a hypothesis test to investigate whether the percent of people in Region X with O positive blood is different from that of in Region W. Which of the following is the appropriate null hypothesis for the investigation? (A) (B) (C) (D) (E) percent confidence interval for the proportion of parents who use parental controls for blocking, filtering, or 143. A . monitoring their teenagers’ online activities is Which of the following could be a percent confidence interval based on the same data? (A) (B) (C) (D) (E) 144. Paul will select a random sample of students to create a 95 percent confidence interval to estimate the proportion of students at his college who have a tattoo. Of the following, which is the smallest sample size that will result in a margin of error of no more than 5 percentage points? Page 54 of 86 AP Statistics Test Booklet 567 (A) 73 (B) 97 (C) 271 (D) 385 (E) 1,537 households and found that the percent confidence 145. Carol, a reporter in a large city, took a random sample of interval for the proportion of households that own a pet is . Jason, the director of a local animal shelter, wants to verify this result for the proportion of households that own a pet and takes a different random households and finds that percent own a pet. sample of Assume the conditions for inference have been met. Jason will calculate a percent confidence interval for the proportion of households that own a pet using his sample data. How would the margin of error from Jason's confidence interval compare to the margin of error from Carol's confidence interval? (A) Jason’s margin of error would be the same as Carol’s margin of error because the confidence level did not change. (B) Jason’s margin of error would be the same as Carol’s margin of error because the point estimate did not change. (C) Jason’s margin of error would be less than Carol’s margin of error because Jason used a smaller sample size. (D) Jason’s margin of error would be greater than Carol’s margin of error because Jason used a smaller sample size. (E) Jason’s margin of error would be greater than Carol’s margin of error because Jason’s point estimate is greater. percent of the students in a certain school district exercise at least 146. An athletic director believes that more than hours per week. To investigate the belief, the director selected a random sample of students in the school district and found that percent of the students in the sample exercise at least hours per week. Let represent the proportion of all students in the school district who exercise at least hours per week. Which of the following is the most appropriate alternative hypothesis to test the director’s claim? (A) (B) (C) (D) (E) 147. The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random versus at the sample of pillows to test. The director tested the hypotheses . The -value of the test was 0.03. Assuming all conditions for inference were met, significance level of which of the following is the correct conclusion? AP Statistics Page 55 of 86 Test Booklet 567 (A) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is less than 0.08. (B) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08. (C) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is greater than 0.08. (D) The -value is less than , and the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08. (E) The -value is less than , and the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of stitching defects is not 0.08. 148. Studies indicate that about 10 percent of polar bears weigh more than 1,000 pounds. A biologist studying the bears thinks that percent might be too high. From a random sample of polar bears, the biologist found only 8 percent of the sample weighing over 1,000 pounds. Which of the following is the most appropriate method for the biologist’s study? (A) A one-sample -test for a sample proportion (B) A one-sample -test for a population proportion (C) A one-sample -test for a difference in population proportions (D) A two-sample -test for a difference in sample proportions (E) A two-sample -test for a difference in population proportions 149. A school librarian wanted to estimate the proportion of students in the school who had read a certain book. The librarian sampled 50 students from the senior English classes, and 35 of the students in the sample had read the book. Have the conditions for creating a confidence interval for the population proportion been met? (A) Yes, because the sample was selected at random. (B) Yes, because sampling distributions of proportions are modeled with the normal model. (C) Yes, because the sample is large enough to satisfy the normality conditions. (D) No, because the sample is not large enough to satisfy the normality conditions. (E) No, because the sample was not selected using a random method. 150. Consider a 90 percent confidence interval for a population proportion . Which of the following is a correct interpretation of the confidence level 90 percent? (A) There is approximately a 90 percent chance that is contained in the interval. (B) There is approximately a 90 percent chance that a randomly selected proportion interval. (C) Approximately 90 percent of all possible sample proportions (D) In repeated samplings with the same sample size, approximately 90 percent of the intervals created will capture the population proportion . (E) In repeated samplings with the same sample size, approximately 90 percent of the intervals created will capture the sample proportion . Page 56 of 86 AP Statistics will be contained in the will be contained in the interval. Test Booklet 567 to estimate the proportion of trees in a 151. A biologist studying trees constructed the confidence interval large forest that are dead but still standing. Using the same confidence level, the interval was later revised because . Which of the following the sample proportion had been miscalculated. The correct sample proportion was statements about the revised interval based on the correct sample proportion is true? (A) The revised interval is narrower than the original interval because the correct sample proportion is farther from than the miscalculated proportion is. (B) The revised interval is narrower than the original interval because the correct sample proportion is closer to than the miscalculated proportion is. (C) The revised interval is wider than the original interval because the correct sample proportion is farther from than the miscalculated proportion is. (D) The revised interval is wider than the original interval because the correct sample proportion is closer to than the miscalculated proportion is. (E) The revised interval has the same width as the original interval. 152. A one-sample -test for a population proportion was conducted to test versus . Assuming the conditions for inference were met, which combination of sample proportion and sample size would result in the smallest -value of the test? (A) and (B) and (C) and (D) and (E) and 153. In high school X, approximately 9 percent of the students saw a certain movie on opening night. From a random sample of 200 students from high school Y, 22 saw the movie on opening night. Consider a hypothesis test to investigate whether the proportion of all students in high school Y who saw the movie on opening night is greater than that of high school X. Which of the following is the standard deviation used to calculate the test statistic for the one-sample -test? (A) (B) (C) (D) (E) 154. A recent study indicated that 17 percent of adults in the country actively seek out science news sites to keep current on topics in science. A university researcher believes that percent is too low. From a random sample of adults in the country, the researcher found that 22 percent of the sample actively seek out science news sites. Which of the following is the most appropriate method for the researcher’s study? AP Statistics Page 57 of 86 Test Booklet 567 (A) A two-sample -test for a difference in population proportions (B) A two-sample -test for a difference in sample proportions (C) A one-sample -test for a difference in population proportions (D) A one-sample -test for a sample proportion (E) A one-sample -test for a population proportion 155. A significance test is conducted for which the alternative hypothesis states that more than 83 percent of all adult sea turtles on a certain beach are female. A random sample of adult sea turtles from the beach found that 85 percent of the sea turtles were female. The -value for the test is 0.4058. If the null hypothesis is true, which of the following statements is a correct interpretation of the -value? (A) Of all possible samples of the same size, 40.58 percent will result in 85 percent of adult sea turtles on the beach being female. (B) Of all possible samples of the same size, 40.58 percent will result in 85 percent or more of adult sea turtles on the beach being female. (C) Of all possible samples of the same size, 40.58 percent will result in 85 percent or less of adult sea turtles on the beach being female. (D) Of all possible samples of the same size, 20.29 percent will result in 85 percent or more of adult sea turtles on the beach being female. (E) Of all possible samples of the same size, 20.29 percent will result in 85 percent of adult sea turtles on the beach being female. 156. To investigate whether more than half the adults in a country are fearful of riding in a self-driving car, researchers surveyed a random sample of adults in the country. Of those in the sample, adults responded that they would be fearful of riding in a self-driving car. Which of the following represents the value of the test statistic for the appropriate hypothesis test for the investigation? (A) (B) (C) (D) (E) 157. Researchers investigating a new drug selected a random sample of 200 people who are taking the drug. Of those selected, 76 indicated they were experiencing side effects from the drug. If 5,000 people took the drug, which of the following is closest to the interval estimate of the number of people who would indicate they were experiencing side effects from the drug at a 90 percent level of confidence? Page 58 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) 158. The manager of a car company will select a random sample of its customers to create a 90 percent confidence interval to estimate the proportion of its customers who have children. Of the following, which is the smallest sample size that will result in a margin of error of no more than 6 percentage points? (A) 100 (B) 125 (C) 150 (D) 200 (E) 275 159. Past studies indicate that about 60 percent of the trees in a forested region are classified as softwood. A botanist studying the region suspects that the proportion might be greater than 0.60. The botanist obtained a random sample versus . The -value of the test was of trees from the region and conducted a test of 0.015. Which of the following is a correct interpretation of the -value? (A) If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6. (B) If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as small as or smaller than the one obtained by the botanist. (C) If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist. (D) If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist. (E) If it is not true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a population proportion greater than 0.6. 160. A marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. The test yielded a -value of 0.47. Assuming all conditions for inference were met, which of the following is the correct conclusion? (A) At the level of significance of 0.05, the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20. (B) At the level of significance of 0.05, the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20. (C) At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to suggest that the true proportion of television viewers who watch the show is less than 0.20. (D) At the level of significance of 0.05, the null hypothesis is rejected. There is not convincing evidence to suggest that the true proportion of television viewers who watch the show is greater than 0.20. (E) At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to conclude that the null hypothesis is true. AP Statistics Page 59 of 86 Test Booklet 567 161. Environmentalists want to estimate the percent of trees in a large forest that are infested with a certain beetle. The environmentalists will select a random sample of trees to inspect. Which of the following is the most appropriate method for creating such an estimate? (A) A two-sample -interval for a population proportion (B) A one-sample -interval for a sample proportion (C) A one-sample -interval for a population proportion (D) A two-sample -interval for a difference between sample proportions (E) A two-sample -interval for a difference between population proportions 162. A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a -value of 0.061. The computation of the -value assumes which of the following is true? (A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. (B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30. (C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30. (D) The population mean number of hours adults spend watching television per week is 15. (E) The population mean number of hours adults spend watching television per week is less than 15. 163. Consider a one-sample two-sided -test for a population proportion. Given that conditions for inference are met, which of the following is closest to the -value for a test statistic of ? (A) 0.0157 (B) 0.0314 (C) 0.0628 (D) 0.9371 (E) 0.9686 164. A recent study on the way that people talk indicated, with 95 percent confidence, that between 35 percent and 41 percent of all adults find the word “whatever” to be the most annoying word in conversation. Based on the confidence interval, which of the following claims is supported? (A) Less than 25 percent of all adults find the word “whatever” to be the most annoying word in conversation. (B) More than 30 percent of all adults find the word “whatever” to be the most annoying word in conversation. (C) More than 45 percent of all adults find the word “whatever” to be the most annoying word in conversation. (D) More than half of all adults find the word “whatever” to be the most annoying word in conversation. (E) At least 95 percent of all adults find the word “whatever” to be the most annoying word in conversation. 165. For a one-sample test for a population proportion are both at least 10 ? Page 60 of 86 AP Statistics and sample size , why is it necessary that and Test Booklet 567 (A) The sample size must be large enough to support an assumption that the distribution of the population is approximately normal. (B) The sample size must be large enough to support an assumption that the distribution of the sample is approximately normal. (C) The sample size must be large enough to support an assumption that the sampling distribution of the sample proportion is approximately normal. (D) The sample size must be large enough to support an assumption that the observations are independent. (E) The sample size must be large enough to support an assumption that the sample proportion is an unbiased estimator of the population proportion. 166. Lila and Robert attend different high schools. They will estimate the population percentage of students at their respective schools who have seen a certain movie. Lila and Robert each select a random sample of students from , their respective schools and use the data to create a 95 percent confidence interval. Lila’s interval is . Which of the following statements can be concluded from the intervals? and Robert’s interval is (A) Lila’s sample size is most likely greater than Robert’s sample size. (B) Robert’s sample size is mostly likely greater than Lila’s sample size. (C) Lila and Robert will both find the same sample proportion of students who have seen the movie. (D) Lila’s interval has a greater degree of confidence than that of Robert. (E) Robert’s interval has a greater degree of confidence than that of Lila. 167. Students in an online course are each randomly assigned to receive either standard practice exercises or adaptive practice exercises. For the adaptive practice exercises, the next question asked is determined by whether the student got the previous question correct. The teacher of the course wants to determine whether there is a difference between the two practice exercise types by comparing the proportion of students who pass the course from each group. The teacher plans to test the null hypothesis that versus the alternative hypothesis , where represents the proportion of students who would pass the course using standard practice exercises and represents the proportion of students who would pass the course using adaptive practice exercises. The teacher knows that the percent confidence interval for the difference in proportion of students passing the course for the two practice exercise types (standard minus adaptive) is and the percent confidence interval for the difference in the proportion of students passing the course for the two practice exercise types . Which of the following is the most reasonable conclusion for the (standard minus adaptive) is teacher’s hypothesis test at the level? (A) The -value is less than , so there is convincing statistical evidence that the proportion of students who would pass the course for the two practice exercise types differs at the level. (B) and , so there is convincing statistical evidence that the proportion of The -value is between level. students who would pass the course for the two practice exercise types differs at the (C) and , so the researchers cannot determine whether the proportion of The -value is between level. students who would pass the course for the two practice exercise types differs at the (D) and , so there is not convincing statistical evidence that the proportion of The -value is between students who would pass the course for the two practice exercise types differs at the level. (E) , so there is not convincing statistical evidence that the proportion of The -value is greater than level. students who would pass the course for the two practice exercise types differs at the AP Statistics Page 61 of 86 Test Booklet 567 168. A department store manager wants to know if a greater proportion of customers on the store’s mailing list would redeem a coupon for $5 off the price of an item than would redeem a coupon for 10 percent off the price of anitem. The manager mails a $5 off coupon to a random sample of 500 customers and mails a 10 percent off coupon to an independent random sample of 500 customers. The number of coupons of each type that were redeemed was recorded. Assuming that the conditions for inference are met, what test procedure should be used to answer the manager’s question? (A) A one-sample t-test for a mean (B) A one-sample z-test for a proportion (C) A t-test for the slope of a regression line (D) A matched-pairs t-test for a mean difference (E) A two-sample z-test for a difference between two proportions 169. A doctor uses a new diagnostic test to indicate whether a patient has a certain disease. The doctor will prescribe medication for the patient if the doctor believes the patient has the disease, as indicated by the diagnostic test. The situation is similar to using a null hypothesis and an alternative hypothesis to decide whether to prescribe the medication. The hypotheses can be stated as follows. : The patient does not have the disease. : The patient has the disease. Which of the following best describes the power of the test? (A) The probability that the new test is better than an older test to indicate whether a patient has the disease (B) The probability that the new test indicates the disease in a patient who has the disease (C) The probability that the new test indicates the disease in a patient who does not have the disease (D) The probability that the new test does not indicate the disease in a patient who has the disease (E) The probability that the new test does not indicate the disease in a patient who does not have the disease 170. A large number of randomized experiments were conducted to determine whether taking a particular drug regularly would decrease the chance of getting a certain disease. For each of the experiments, the drug effect is the difference between the proportion of people taking the drug who got the disease and the proportion of people taking a placebo who got the disease. If the drug had no effect whatsoever, which of the following experimental results would be anticipated? I. p-values will be greater than 0.05 for about 95 percent of the experiments. II. There will be about an equal number of experiments showing positive and negative values of drug effect. III. When 95 percent confidence intervals for the population drug effect are constructed, those confidence intervals include 0 about 95 percent of the time. Page 62 of 86 AP Statistics Test Booklet 567 (A) I only (B) II only (C) III only (D) I and II only (E) I, II and III 171. A medical doctor uses a diagnostic test to determine whether a patient has arthritis. A treatment will be prescribed only if the doctor thinks the patient has arthritis. The situation is similar to using a null and an alternative hypothesis to decide whether to prescribe the treatment. The hypotheses might be stated as follows. H0 : The patient does not have arthritis Ha : The patient has arthritis Which of the following represents a Type II error for the hypotheses? (A) Diagnosing arthritis in a patient who has arthritis (B) Failing to diagnose arthritis in a patient who has arthritis (C) Diagnosing arthritis in a patient who does not have arthritis (D) Failing to diagnose arthritis in a patient who does not have arthritis (E) Prescribing treatment to a patient regardless of the diagnosis 172. An environmental scientist wants to test the null hypothesis that an antipollution device for cars is not effective. Under which of the following conditions would a Type I error be committed? (A) The scientist concludes that the antipollution device is effective when it actually is not. (B) The scientist concludes that the antipollution device is not effective when it actually is. (C) The scientist concludes that the antipollution device is effective when it actually is. (D) The scientist concludes that the antipollution device is not effective when it actually is not. (E) A Type I error cannot be committed in this situation. 173. A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true? (A) Neither the probability of a Type II error nor the power of the test would change. (B) Both the probability of a Type II error and the power of the test would decrease. (C) Both the probability of a Type II error and the power of the test would increase. (D) The probability of a Type II error would decrease and the power of the test would increase. (E) The probability of a Type II error would increase and the power of the test would decrease. AP Statistics Page 63 of 86 Test Booklet 567 174. A police officer uses a motion detector to indicate whether a car is traveling faster than the speed limit (speeding). A speeding ticket will be issued to the driver of the car if the officer believes the driver is speeding, as indicated by the detector. The situation is similar to using a null and an alternative hypothesis to decide whether to issue a ticket. The hypotheses can be stated as follows. H0 : The driver is not speeding. Ha : The driver is speeding. Which of the following best describes the power of the test? (A) The probability of issuing a ticket to a driver who is speeding (B) The probability of issuing a ticket to a driver who is not speeding (C) The probability of not issuing a ticket to a driver who is speeding (D) The probability of not issuing a ticket to a driver who is not speeding (E) The probability that the motion detector is working correctly 175. There are 1,000 golden delicious and 1,000 red delicious apples in a cooler. In a random sample of 75 of the golden delicious apples, 48 had blemishes. In a random sample of 75 of the red delicious apples, 42 had blemishes. Assume all conditions for inference have been met. Which of the following is closest to the interval estimate of the difference in the numbers of apples with blemishes (golden delicious minus red delicious) at a 98 percent level of confidence? (A) (B) (C) (D) (E) 176. Two voting districts, C and M, were sampled to investigate voter opinion about tax spending. From a random sample of 100 voters in District C, 22 percent responded yes to the question “Are you in favor of an increase in state spending on the arts?” An independent random sample of 100 voters in District M resulted in 26 percent responding yes to the question. A 95 percent confidence interval for the difference was calculated as . Which of the following is the best interpretation of the interval? Page 64 of 86 AP Statistics Test Booklet 567 (A) We are 95% confident that the majority of all voters in the state favor an increase in state spending for the arts. (B) We are 95% confident that less than half of all voters in the state favor an increase in state spending for the arts. (C) We are 95% confident that the difference in the proportions of all voters in districts C and M who favor an and 0.08. increase in state spending for the arts is between (D) We are 95% confident that the difference in the sample proportions of voters in districts C and M who favor an increase in state spending for the arts is between and 0.08. (E) We are 95% confident that the proportion of all voters in the state who favor an increase in state spending for and 0.08. the arts is between 177. As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Of the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers? (A) (B) (C) (D) (E) 178. A factory manager selected a random sample of parts produced on an old assembly line and a random sample of parts produced on a new assembly line. The difference between the sample proportion of defective parts made on the old assembly line and the sample proportion of defective parts made on the new assembly line (old minus new) was 0.006. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being the proportion of defective parts made on the old assembly line is greater than that of the new assembly line. The -value of the test was 0.018. Which of the following is the correct interpretation of the -value? (A) If there is a difference of 0.018 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.006. (B) If there is a difference of 0.006 in the proportions of all defective parts made on the two assembly lines, the probability of observing that difference is 0.018. (C) If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference equal to 0.006 is 0.018. (D) If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at least 0.006 is 0.018. (E) If there is no difference in the proportions of all defective parts made on the two assembly lines, the probability of observing a difference of at most 0.006 is 0.018. AP Statistics Page 65 of 86 Test Booklet 567 179. A survey was conducted in a large city to investigate public opinion on banning the use of trans fats in restaurant cooking. A random sample of 230 city residents with school-age children was selected, and another random sample of 341 city residents without school-age children was also selected. Of those with school-age children, 94 opposed the banning of trans fats, and of those without school-age children, 147 opposed the banning of trans fats. An appropriate hypothesis test was conducted to investigate whether there was a difference between the two groups of residents in their opposition to the banning of trans fats. Is there convincing statistical evidence of a difference between the two population proportions at the significance level of 0.05 ? (A) Yes, because the sample proportions are different. (B) Yes, because the probability of observing a difference at least as large as the sample difference is greater than 0.05. (C) Yes, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is less than 0.05. (D) No, because the probability of observing a difference at least as large as the sample difference, if the two population proportions are the same, is greater than 0.05. (E) No, because the probability of observing a difference at least as large as the sample difference is less than 0.05. 180. A university will add fruit juice vending machines to its classroom buildings if the student body president is convinced that more than 20 percent of the students will use them. A random sample of n students will be selected and asked whether or not they would use the vending machines. A large-sample test for proportions at the significance level of α = 0.05 will be performed. The null hypothesis that the proportion of all students who would use the vending machines is 20 percent will be tested against the alternative that more than 20 percent of all students would use them. For which of the following situations would the power of the test be highest? (A) The sample size is n = 750, and 20 percent of all students use the vending machines. (B) The sample size is n = 750, and 25 percent of all students use the vending machines. (C) The sample size is n = 1,000, and 25 percent of all students use the vending machines. (D) The sample size is n = 500, and 50 percent of all students use the vending machines. (E) The sample size is n = 1,000, and 50 percent of all students use the vending machines. , percent of a random sample of adults in the United States indicated that they consumed at least 181. In pounds of bacon that year. In , percent of a random sample of adults in the United States indicated that they consumed at least pounds of bacon that year. Assuming all conditions for inference are met, which of the following is the most appropriate test statistic to use to investigate whether the proportion of all adults in the United States who consume at least pounds of bacon in is different from that of ? Page 66 of 86 AP Statistics Test Booklet 567 (A) (B) (C) (D) (E) 182. Two large containers, X and Y, contain many colored beads. From a random sample of beads taken from container X, the proportion of blue beads in the sample was recorded as . From a random sample of beads taken from container Y, the proportion of blue beads in the sample was recorded as . Assuming all conditions for inference are met, which of the following procedures is the most appropriate for estimating the difference between the proportions of all blue beads in the containers? (A) A two-sample -interval for a difference in population proportions (B) A two-sample -interval for a difference in sample proportions (C) A one-sample -interval for a population proportion (D) A one-sample -interval for a sample proportion (E) A one-sample -interval for a difference in population proportions 183. For a chi-square test for independence with degrees of freedom and a significance level of test statistic was . The associated -value was . , the value of the Assuming all necessary conditions for the chi-square test were met, what type of error is possible? (A) A Type error is possible, because the null hypothesis was rejected. (B) A Type error is possible, because the null hypothesis was not rejected. (C) No error is possible, because the correct decision was made. (D) A Type error is possible, because the null hypothesis was rejected. (E) error is possible, because the null hypothesis was not rejected. A Type 184. A researcher calculated sample proportions from two independent random samples. Assuming all conditions for inference are met, which of the following is the best method for the researcher to use to estimate the true difference between the population proportions? (A) Construct a two-sample -interval for the difference between population proportions. (B) Construct a two-sample -interval for the difference between sample proportions. (C) Perform a -test for the difference in sample proportions. (D) Subtract the proportions and construct a one-sample -interval for a single population proportion. (E) Subtract the proportions and construct a -interval for a single sample proportion. AP Statistics Page 67 of 86 Test Booklet 567 people who had been diagnosed as prediabetic because of high blood glucose levels volunteered to 185. A group of participate in a study designed to investigate the use of cinnamon to reduce blood glucose to a normal level. Of the people, were randomly assigned to take a cinnamon tablet each day and the other were assigned to take a placebo each day. The people did not know which tablet they were taking. Their blood glucose levels were people in the cinnamon group and people in the measured at the end of one month. The results showed that placebo group had normal blood glucose levels. For people similar to those in the study, do the data provide convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon? (A) No conclusion can be made about the use of cinnamon because the people in the study were volunteers. (B) There is convincing statistical evidence at the level of . (C) There is convincing statistical evidence at the level of but not at the level of . (D) There is convincing statistical evidence at the level of but not at the level of . (E) There is not convincing statistical evidence at any reasonable significance level. 186. In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1 = p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion? (A) There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05. (B) There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the z-test statistic is greater than 0.05. (C) There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05. (D) There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is less than 0.05. (E) There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is greater than the proportion of all overweight dogs in Colorado because the z-test statistic is positive. 187. Suppose a hypothesis test will be used to investigate whether the proportion of United States adults who have been a victim of a cybercrime, such as identity theft, is greater than . Suppose that the hypothesis test is conducted using a significance level of and the power of the test is determined for a specific alternative value using the significance level of . and the power of the test is computed for the same If the significance level of the hypothesis test is changed to alternative value using a significance level of , which of the following best describes the change(s) to the probability of a Type error and the power of the test? (A) The probability of a Type error would decrease, and the power of the test would stay the same. (B) The probability of a Type error would decrease, and the power of the test would increase. (C) The probability of a Type error would decrease, and the power of the test would decrease. (D) The probability of a Type error would increase, and the power of the test would increase. (E) Page 68 of 86 The probability of a Type error would increase, and the power of the test would decrease. AP Statistics Test Booklet 567 188. A statistical test involves the following null and alternative hypotheses. Which of the following describes a Type error? (A) Failing to reject the null hypothesis when the population mean is (B) Failing to reject the null hypothesis when the population mean is greater than (C) Rejecting the null hypothesis when the population mean is (D) Rejecting the null hypothesis when the population mean is greater than (E) Failing to reject the null hypothesis when the -value is less than the significance level 189. Market researchers interviewed a random sample of 60 men and a random sample of 55 women about their preferences for different color designs for the packaging of a certain product. Of those interviewed, 23 men and 28 women preferred color design X. Which of the following is the correct test statistic for a two-sample -test for a difference in population proportions for men and women (men minus women) in their preference for color design X ? (A) (B) (C) (D) (E) 190. Consider a 95 percent confidence interval constructed for the difference between two population proportions and . The interval for is given as . Which of the following is an appropriate interpretation of the confidence level? (A) In repeated random sampling with the same sample size, approximately 95 percent of the time. (B) In repeated random sampling with the same sample size, 95 percent of the time. will be contained in the interval approximately (C) In repeated random sampling with the same sample size, 95 percent of the time. will be contained in the interval approximately will be contained in the interval (D) The probability is 0.95 that the difference in the sample proportions (E) is between and 0.15. In repeated random sampling with the same sample size, approximately 95 percent of the intervals will capture the difference in population proportions, . AP Statistics Page 69 of 86 Test Booklet 567 191. To investigate whether there is a difference in opinion on a certain proposal between two voting districts, A and B, two independent random samples were taken. From district A, 35 of the 50 voters selected were in favor of the proposal, and from district B, 36 of the 60 voters selected were in favor of the proposal. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in the proportion of voters who are in favor of the proposal between the two districts (district A minus district B)? (A) (B) (C) (D) (E) 192. Independent random samples of voters from two voting districts, G and H, were selected to investigate the proportion of all voters who favor a proposal to widen a road that runs through both districts. The difference between the sample proportions (G minus H) was used to create the 95 percent confidence interval the population difference between districts. for Which of the following is the best interpretation of the interval? (A) It is likely that the majority of voters in both districts favor the proposal, because all values in the interval are positive. (B) It is likely that more voters in district H favor the proposal than in district G, because all values in the interval are positive. (C) It is likely that more voters in district G favor the proposal than in district H, because all values in the interval are positive. (D) It is likely that less than half the voters in both districts favor the proposal, because all values in the interval are less than 0.5. (E) It is likely that there is no difference between the districts in voters who favor the proposal, because 0 is not contained in the interval. Page 70 of 86 AP Statistics Test Booklet 567 residents from a suburban area of the county and a separate 193. A county manager selected a random sample of random sample of residents from an urban area of the same county. The residents in the samples were asked whether they thought the county should create dog parks where residents can take their dogs to play. From those percent of the suburban residents and percent of the urban residents thought the county who were sampled, should create dog parks. Let represent the population proportion of suburban residents who think the county should create dog parks, and let represent the population proportion of urban residents who think the county should create dog parks. The county manager will test the following hypotheses. Assuming the conditions for inference were met, which of the following is closest to the -value of the county manager’s test? (A) (B) (C) (D) (E) 194. A study was conducted to investigate whether a new drug could significantly reduce pain in people with arthritis. From a group of 500 people with arthritis, 250 were randomly assigned to receive the drug (group 1) and the remaining people were assigned a placebo (group 2). After one month of treatment, 225 people in group 1 reported pain relief and 150 people in group 2 reported pain relief. Let represent the combined (or pooled) sample proportion for the two samples. Have the conditions for inference for testing the difference in population proportions been met? (A) No. The people in the study were not selected at random. (B) No. The number of people in the study was too large compared with the size of the population. (C) No. The normality of the sampling distribution cannot be assumed because sufficiently large. (D) No. The normality of the sampling distribution cannot be assumed because not sufficiently large. (E) Yes. All conditions for inference have been met. times each sample size is not times each sample size is 195. Which of the following gives the probability of making a Type error? AP Statistics Page 71 of 86 Test Booklet 567 (A) The sample size (B) The power (C) The significance level (D) The standard error (E) The -value 196. Consider the results of a hypothesis test, which indicate there is not enough evidence to reject the null hypothesis. Which of the following statements about error is correct? (A) A Type error could have been made, but not a Type error. (B) A Type (C) Both types of error could have been made, but the probability of a Type error is greater than the probability of a Type error. (D) Both types of error could have been made, but the probability of a Type error is less than the probability of a Type error. (E) The type of error that could have been made is not possible to determine without knowing the statement of the null hypothesis. error could have been made, but not a Type error. 197. At a manufacturing company for medical supplies, machines produce parts used in highly specialized lasers. Company researchers are testing a new machine designed to improve the precision of the parts. The null hypothesis is that the new machine does not improve the precision. For the researchers, the more consequential error would be that the new machine actually improves the precision, but the test does not detect the improvement. Which of the following should the researchers do to avoid the more consequential error? (A) Increase the significance level to increase the probability of a Type error. (B) Increase the significance level to decrease the probability of a Type error. (C) Decrease the significance level to increase the probability of a Type error. (D) Decrease the significance level to decrease the probability of a Type error. (E) Decrease the significance level to decrease the standard error. 198. Machines at a bottling plant are set to fill bottles to 12 ounces. The quality control officer at the plant periodically tests the machines to be sure that the bottles are filled to an appropriate amount. The null hypothesis of the test is that the mean is at least 12 ounces. The alternative hypothesis is that the mean is less than 12 ounces. Which of the following describes a Type error that could result from the test? (A) The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. (B) The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is less than 12 ounces. (C) The test does not provide convincing evidence that the mean is less than 12 ounces, but the actual mean is 12 ounces. (D) The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is at least 12 ounces. (E) The test provides convincing evidence that the mean is less than 12 ounces, but the actual mean is 11 ounces. Page 72 of 86 AP Statistics Test Booklet 567 199. Researchers were investigating whether there is a significant difference between two medications, R and S, designed to reduce fleas found on cats. From a sample of 300 cat owners, the researchers randomly assigned 150 cat owners to use medication R on their cats and the remaining cat owners to use medication S. For the cats using medication R, 88 percent had no fleas. For the cats using medication S, 90 percent had no fleas. Which of the following is the most appropriate method for analyzing the results? (A) A two-sample -test for a difference in population proportions (B) A two-sample -test for a difference in sample proportions (C) A one-sample -test for a sample proportion (D) A one-sample -test for a population proportion (E) A one-sample -test for a difference in sample proportions randomly selected adults who are not scientists and randomly 200. A polling organization surveyed selected adults who are scientists. Each adult was asked the question, “Do you think that genetically modified foods are safe to eat?” Of those who are not scientists, percent responded yes, and of those who are scientists, percent responded yes. Which of the following is the standard error used to construct a confidence interval for the difference between the proportions of all adults who are not scientists and all adults who are scientists who would answer yes to the question? (A) (B) (C) (D) (E) 201. The mayor of a large city will run for governor if he believes that more than 30 percent of the voters in the state already support him. He will have a survey firm ask a random sample of n voters whether or not they support him. He will use a large sample test for proportions to test the null hypothesis that the proportion of all voters who support him is 30 percent or less against the alternative that the percentage is higher than 30 percent. Suppose that 35 percent of all voters in the state actually support him. In which of the following situations would the power for this test be highest? (A) The mayor uses a significance level of 0.01 and n = 250 voters. (B) The mayor uses a significance level of 0.01 and n = 500 voters. (C) The mayor uses a significance level of 0.01 and n = 1,000 voters. (D) The mayor uses a significance level of 0.05 and n = 500 voters. (E) The mayor uses a significance level of 0.05 and n = 1,000 voters. AP Statistics Page 73 of 86 Test Booklet 567 202. A sociologist studying teen behavior took independent random samples of students from two high schools, F and G. Of the 80 students selected from High School F, 36 indicated they had seen a certain movie. Of the 72 students selected from High School G, 18 indicated they had seen the movie. Which of the following is the test statistic for the appropriate test to investigate whether there is a difference in population proportions (High School F minus High School G) ? (A) (B) (C) (D) (E) 203. In 1960 sociologists studied a random sample of 1,018 families that consisted of a husband, a wife, and at least one child. Of those families, 5.8 percent reported that the wife was the primary wage earner of the family. In 2011 the study was replicated with a random sample of 1,013 families that consisted of a husband, a wife, and at least one child. Of those families, 22.3 percent reported that the wife was the primary wage earner of the family. Which of the following represents a 99 percent confidence interval for the difference between the proportions of families that consisted of a husband, a wife, and at least one child from 1960 to 2011 that would have reported the wife as the primary wage earner? (A) (B) (C) (D) (E) 204. In a random sample of 60 shoppers chosen from the shoppers at a large suburban mall, 36 indicated that they had been to a movie in the past month. In an independent random sample of 50 shoppers chosen from the shoppers in a large downtown shopping area, 31 indicated that they had been to a movie in the past month. What significance test should be used to determine whether these data provide sufficient evidence to reject the hypothesis that the proportion of shoppers at the suburban mall who had been to a movie in the past month is the same as the proportion of shoppers in the large downtown shopping area who had been to a movie in the past month? Page 74 of 86 AP Statistics Test Booklet 567 (A) One proportion z-test (B) One sample z-test for a mean (C) One sample t-test for a mean (D) Two proportion z-test (E) Two sample t-test for means 205. At a large company, employees can take a course to become certified to perform certain tasks. There is an exam at the end of the course that needs to be passed for certification. The current pass rate is 0.7, but a new program is being tested to help increase the pass rate. The null hypothesis of the test is that the pass rate for the new program is 0.7. The alternative is that the pass rate for the new program is greater than 0.7. Which of the following describes a Type error that could result from the test? (A) The test does not provide convincing evidence that the pass rate is greater than 0.7, but the actual pass rate is 0.8. (B) The test does not provide convincing evidence that the pass rate is greater than 0.7, but the actual pass rate is 0.7. (C) The test does not provide convincing evidence that the pass rate is greater than 0.7, but the actual pass rate is 0.6. (D) The test provides convincing evidence that the pass rate is greater than 0.7, but the actual pass rate is 0.8. (E) The test provides convincing evidence that the pass rate is greater than 0.7, but the actual pass rate is 0.6. 206. Because library books are read many times, glue is often applied to the spine of a book to keep the pages tight. A glue is considered successful if a book lasts at least 6 months before needing to be reglued. Two brands of glue, G and K, were tested to determine whether there was a difference in the proportion of books lasting at least 6 months. Let represent the proportion of books lasting at least 6 months when glued with G, and let represent the proportion of books lasting at least 6 months when glued with K. The following hypothesis test was conducted at . the significance level of All conditions for inference were met, and the resulting -value was 0.006. Which of the following is the correct decision for the test? AP Statistics Page 75 of 86 Test Booklet 567 The -value is less than , and the null hypothesis is rejected. There is not convincing evidence to support (A) the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. (B) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. (C) The -value is less than , and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. The -value is greater than , and the null hypothesis is rejected. There is convincing evidence to support the (D) claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. (E) The -value is greater than , and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K. 207. The police in a certain city are investigating whether the proportion of minor traffic accidents is greater on Friday nights than on Sunday nights. As part of the investigation, they select a random sample of police calls from Friday nights and a random sample of police calls from Sunday nights. From both samples, they record the sample represent the proportion of all Friday night calls, proportion of calls that involved minor traffic accidents. Let represent the proportion of all Sunday night calls. Which of the following are the correct hypotheses for and let the investigation? (A) (B) (C) (D) (E) 208. Market researchers selected a random sample of people from region A and a random sample of people from region B. The researchers asked the people in the samples whether they had tried a new product. The difference between the sample proportions (B minus A) of people in the regions who indicated they had tried the new product was 0.15. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportion of B is greater than that of A. The -value of the test was 0.34. Which of the following is the correct interpretation of the -value? Page 76 of 86 AP Statistics Test Booklet 567 (A) If the difference in proportions of people who have tried the new product between the two populations is actually 0.15, the probability of observing that difference is 0.34. (B) If the difference in proportions of people who have tried the new product between the two populations is actually 0.34, the probability of observing that difference is 0.15. (C) If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at least 0.15 is 0.34. (D) If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference of at most 0.15 is 0.34. (E) If the proportions of all people who have tried the new product is the same for both regions, the probability of observing a difference equal to 0.15 is 0.34. 209. Market researchers wanted to know whether the placement of a new product on a supermarket shelf significantly increases the percent of shoppers who will buy the product. At Supermarket X, a new product was placed on the top shelf, and at Supermarket Y, the product was placed one shelf below the top shelf. To observe buying habits, the researchers selected a random sample of 364 shoppers at X and another random sample of 327 shoppers at Y. Of the selected shoppers at X, 15 bought the product, and of the selected shoppers at Y, 19 bought the product. Which of the following is the most appropriate method for analyzing the results? (A) A two-sample -test for a difference in sample proportions (B) A two-sample -test for a difference in population proportions (C) A one-sample -test for a sample proportion (D) A one-sample -test for a population proportion (E) A one-sample -test for a difference in sample proportions 210. Which of the following is not a condition for constructing a confidence interval to estimate the difference between two population proportions? (A) The samples must be selected randomly. (B) The data must come from populations with approximately normal distributions. (C) When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample. (D) The samples must be independent of each other. (E) The observed number of successes and failures for both samples must be at least 10. 211. Polydactyl cats are cats with extra toes. A researcher believes that the proportion of the population of polydactyl cats in region A is greater than the proportion in region B. Let represent the population proportion of polydactyl represent the population proportion of polydactyl cats in region B. Which of the cats in region A, and let following are the appropriate hypotheses to test the researchers belief? AP Statistics Page 77 of 86 Test Booklet 567 (A) (B) (C) (D) (E) 212. Consider a hypothesis test in which the significance level is probability of making a Type error? and the power of the test is 0.65. What is the (A) 0.95 (B) 0.65 (C) 0.60 (D) 0.35 (E) 0.05 213. A recent study was conducted in which a random sample of men and a random sample of women were surveyed about whether they were fans of a professional football team. The study found that 39 percent of men in the sample were fans and 22 percent of women in the sample were fans. A 99 percent confidence interval for the difference in . the proportion of fans of a professional football team between men and women was reported as Which of the following statements is the best interpretation of the interval? (A) The difference in the percents of fans of a professional football team between men and women is 17%. (B) There is a 99% chance of finding a difference between 13.3% and 20.7% for the percents of men and women who are fans of a professional football team. (C) We are 99% confident that the percent of men who are fans of a professional football team exceeds that of women by at least 20.7%. (D) We are 99% confident that the difference in the sample percents of men and women who are fans of a professional football team is between 13.3% and 20.7%. (E) We are 99% confident that the difference in the population percents of all men and women who are fans of a professional football team is between 13.3% and 20.7%. Page 78 of 86 AP Statistics Test Booklet 567 214. Maria has two routes, E and W, she can take when commuting to work. Both routes go through a railroad crossing, and sometimes she needs to stop at the crossing to allow trains to pass. She claims that the proportion of times she needs to stop when taking route E is different from the proportion of times she needs to stop when taking route W. . She conducted the following hypothesis test at the significance level of In the hypotheses, represents the proportion of times she needs to stop at the crossing when using route E, and represents the proportion of times she needs to stop at the crossing when using route W. All conditions for inference were met, and the resulting -value was 0.37. Which of the following is the correct decision for the test? (A) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes. (B) The -value is greater than , and the null hypothesis is not rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is the same for the different routes. (C) The -value is greater than , and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes. The -value is greater than , and the null hypothesis is not rejected. There is not convincing evidence to (D) support the claim that the proportion of times she needs to stop at the crossing is different for the different routes. (E) The -value is greater than , and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of times she needs to stop at the crossing is different for the different routes. 215. A biologist wants to compare the proportions of rainbow trout infected with whirling disease (an illness of trout and salmon caused by a microscopic parasite) coming from two separate watersheds. For each watershed, the biologist will collect a random sample of trout and record the proportion infected in the sample. The biologist intends to estimate the difference for all trout in the two watersheds. Assuming all conditions for inference are met, which of the following is the most appropriate method for the biologist to use to analyze the results? (A) A one-sample -interval for a population proportion (B) A one-sample -interval for a sample proportion (C) A one-sample -interval for a difference in sample proportions (D) A two-sample -interval for a difference in population proportions (E) A two-sample -interval for a difference in sample proportions 216. Educators are testing a new program designed to help children improve their reading skills. The null hypothesis of the test is that the program does not help children improve their reading skills. For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help. Which of the following should the researchers do to avoid the more consequential error? AP Statistics Page 79 of 86 Test Booklet 567 (A) Increase the significance level to increase the probability of Type error. (B) Increase the significance level to decrease the probability of Type error. (C) Decrease the significance level to increase the probability of Type error. (D) Decrease the significance level to decrease the probability of Type error. (E) Decrease the significance level to decrease the standard error. 217. A 95 percent confidence interval for the proportion difference was calculated to be . Which of the following conclusions is supported by the interval? (A) There is evidence to conclude that because 0.17 is greater than . (B) There is evidence to conclude that because 0.17 is greater than 0.12. (C) There is evidence to conclude that the range of negative values. because the range of positive values in the interval is greater than (D) There is evidence to conclude that the range of negative values. because the range of positive values in the interval is greater than (E) There is not sufficient evidence to determine which proportion is greater. 218. Two locations of a fast-food restaurant, Location Q and Location W, were in a certain town with a large number of residents. A nutritionist investigated whether the proportion of orders that contained a salad was different at the two locations. The nutritionist obtained a random sample of orders from the Location Q restaurant and a random sample of orders from the Location W restaurant. Of the 215 Location Q orders, 27 contained a salad; of the 175 Location W orders, 14 contained a salad. Let represent the combined sample proportion, and let and represent the respective sample sizes for Locations Q and W. Have the conditions for inference for testing a difference in population proportions been met? (A) No, the condition for independence has not been met because random samples were not selected from each location. (B) No, the condition for independence has not been met because the sample sizes are too large when compared to the corresponding population sizes. (C) No, the condition that the sampling distribution of the difference in sample proportions is approximately is not greater than 10. normal has not been met because No, the condition that the sampling distribution of the difference in sample proportions is approximately (D) normal has not been met because is not greater than 10. (E) Yes, all conditions for making statistical inference have been met. 219. Consider a situation in which sampling without replacement is used to generate a random sample from each of two separate populations. To calculate a confidence interval to estimate the difference between population proportions, which of the following checks must be made? (A) Each population must be at least 10 times as large as its corresponding sample. (B) Both populations must be approximately normal. (C) The data from both samples must be unimodal, symmetrical, and approximately normal. (D) Each sample proportion value must be less than or equal to 0.5. (E) Page 80 of 86 The sample sizes must be the same. AP Statistics Test Booklet 567 220. A service company recently revised its call-routing procedures in an attempt to increase efficiency in routing customer calls to the appropriate agents. A random sample of customer calls was taken before the revision, and another random sample of customer calls was taken after the revision. The selected customers were asked if they were satisfied with the service call. The difference in the proportions of customers who indicated they were satisfied was calculated. A 90 percent confidence interval for the difference is given as . The manager of the company claims that the revision in procedure will change the proportion of customers who will indicate satisfaction with their calls. Does the confidence interval support the manager’s claim? (A) No. The value of 0 is contained in the interval, which indicates that it is plausible that there is no difference in the proportion of customers who will indicate satisfaction with their calls. (B) No. All values in the interval are less than 0.12, which indicates that the difference in the proportion of customers who will indicate satisfaction with their calls is very small. (C) Yes. There are more positive values in the interval than negative values, which indicates that more customers indicated satisfaction with their calls after the revision. (D) Yes. The length of the interval is greater than 0.10, which indicates that the sample difference in the proportion of customers who will indicate satisfaction with their calls is plausible. (E) Yes. The value of 0 is contained in the interval, which indicates that a difference in the proportion of customers who will indicate satisfaction with their calls is plausible. 221. A local school board wanted to investigate whether their approval ratings had changed during the past year. The board selected random samples of voters at both the beginning and the end of the year, and each time the voters represent the proportion of voters who approved of the were asked whether they approve of the school board. Let school board at the beginning of the year and represent the proportion of voters who approved of the school board at the end of the year. Which of the following are the correct null and alternative hypotheses for the school board’s investigation? (A) (B) (C) (D) (E) AP Statistics Page 81 of 86 Test Booklet 567 222. A gardener wants to know if soaking seeds in water before planting them increases the proportion of seeds that germinate. To investigate, the gardener will assign 50 seeds to be soaked before planting and 50 seeds to be planted without being soaked. After two weeks, the gardener will record how many seeds in each group germinated and construct a 95 percent confidence interval for the difference in proportions. Which of the following conditions for inference should be met? I. The seeds should be randomly assigned to a treatment. II. The group sizes should be less than 10 percent of the population sizes. III. The number of successful seeds and unsuccessful seeds in each group should be at least 10. (A) only (B) only only (C) (D) and (E) , only , and 223. Suppose that on a hypothesis test for a single population mean, Ha: μ < 10. Assume that Ha is true. For a fixed sample size and significance level α, the power of the test will be greatest if the actual mean is which of the following? (A) 8 (B) 9 (C) 10 (D) 11 (E) 13 224. Biologists were studying the proportions of cats that had spotted markings on their fur in two populations of cats, C and F. An independent random sample of cats was taken from each population, and the difference between the sample proportions of cats with the spotted markings (C minus F) was 0.62. Under the assumption that all conditions for inference were met, a hypothesis test was conducted with the alternative hypothesis being that the population proportions are not equal. The -value of the test was 0.01. Which of the following is the correct interpretation of the -value? (A) If the proportions of all cats with spotted markings is the same for both populations, the probability of is 0.01. observing a sample difference of at least 0.62 or at most (B) If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at least 0.62 is 0.01. (C) If the proportions of all cats with spotted markings is the same for both populations, the probability of observing a sample difference of at most is 0.01. (D) If the difference in proportions of cats with spotted markings between the two populations is actually 0.62, the probability of observing that difference is 0.01. (E) If the difference in proportions of cats with spotted markings between the two populations is actually 0.01, the probability of observing that difference is 0.62. Page 82 of 86 AP Statistics Test Booklet 567 225. Researchers are studying the distribution of subscribers to a certain streaming service in different populations. From a random sample of 200 people in City C, 34 were found to subscribe to the streaming service. From a random sample of 200 people in City K, 54 were found to subscribe to the streaming service. Assuming all conditions for inference are met, which of the following is a 90 percent confidence interval for the difference in population proportions (City C minus City K) who subscribe to the streaming service? (A) (B) (C) (D) (E) 226. From a random sample of 185 children from school G, 108 indicated they wanted to study science in college. From a different random sample of 165 children from school H, 92 indicated they wanted to study science in college. Assuming all conditions for inference are met, which of the following is closest to the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college? (A) (B) (C) (D) (E) 227. Medical researchers are testing a new surgical procedure designed to minimize the side effects of surgery. The null hypothesis is that the procedure is not effective in minimizing side effects. For the researchers, the more consequential error would be that the procedure actually is effective in minimizing the side effects, but the test does not detect the effectiveness of the procedure. Which of the following should the researchers do to avoid the more consequential error? (A) Increase the significance level to increase the probability of a Type error. (B) Increase the significance level to decrease the probability of a Type error. (C) Decrease the significance level to increase the probability of a Type error. (D) Decrease the significance level to decrease the probability of a Type error. (E) Decrease the significance level to decrease the standard error. AP Statistics Page 83 of 86 Test Booklet 567 228. If all else is constant, which of the following would result in a decrease of the probability of a Type error? (A) The true parameter is closer to the null. (B) The sample size is increased. (C) The significance level is decreased. (D) The standard error is increased. (E) Type error cannot be decreased, only increased. 229. A one-sample -test for a proportion at the significance level of of hypotheses. For which of the following is the probability of a Type (A) A sample size of and a true proportion of (B) A sample size of and a true proportion of (C) A sample size of and a true proportion of (D) A sample size of and a true proportion of (E) and a true proportion of A sample size of will be conducted for the following set error the greatest? 230. The following list shows three factors that can either increase or decrease the probability of a Type error. I. The sample size is increased. II. The significance level is increased. III. The standard error is increased. Which factors alone will cause the probability of a Type (A) error to increase? only (B) only (C) only (D) and (E) , only , and 231. If all else is constant, which of the following results in an increase in the probability of a Type (A) The significance level is increased. (B) The standard error is decreased. (C) The probability of a Type error cannot be increased, only decreased. (D) The true parameter is farther from the null hypothesis. (E) Page 84 of 86 The sample size is decreased. AP Statistics error? Test Booklet 567 232. Researchers from a national research organization investigated which platform (television, social media, newspaper, Internet, etc.) United States adults prefer to use to obtain their news. In , of the randomly selected United States adults that were surveyed, selected television as their preferred platform. In , of the randomly selected television as their preferred platform. The conditions selected United States adults that were surveyed, for inference are met. A percent confidence interval for the difference in the population proportions of United States adults that use television as their preferred platform for obtaining news between and minus was found to be . Based on the interval, is it reasonable for the researchers to claim that there is convincing statistical evidence that the population proportion of United States adults that use television as their preferred method to obtain news differed between and ? (A) No, because the researchers should have used a greater confidence level to obtain convincing evidence. (B) No, because zero is included in the interval there is not convincing statistical evidence that the population proportion differed between and . (C) Yes, because zero is included in the interval there is convincing statistical evidence that the population proportion differed between and . (D) Yes, because most of the interval is positive there is convincing statistical evidence that the population proportion increased from to . (E) Yes, because decreased from is greater than to . there is convincing statistical evidence that the population proportion 233. To investigate whether there is a significant difference between two regions of a state in the percent of voters who intend to vote for the incumbent governor in the next election, a polling agency interviewed 300 randomly selected voters from the north of the state and 400 randomly selected voters from the south of the state. Of those interviewed, 200 from the north and 325 from the south indicated they intended to vote for the incumbent governor in the next election. Which of the following is the most appropriate method for analyzing the results? (A) A one-sample -test for a sample proportion (B) A one-sample -test for a population proportion (C) A two-sample -test for a sample proportion (D) A two-sample -test for a difference in sample proportions (E) A two-sample -test for a difference in population proportions 234. A political scientist claims that negative advertising on television affects younger voters more than it affects older voters. To test this claim, the scientist obtained data from two random samples of voters categorized into two agegroups, older and younger. The null hypothesis was that there was no difference in the proportions of voters in the two age-groups who would be affected by negative ads. The alternative hypothesis was that the proportion of younger voters affected would be greater than the proportion of older voters affected. Assuming all conditions for inference were met, the scientist conducted the test at a significance level of The resulting -value was 0.206. Which of the following is the correct decision for the test? AP Statistics . Page 85 of 86 Test Booklet 567 (A) The -value is less than , and the null hypothesis is rejected. There is convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. (B) The -value is less than , and the null hypothesis is rejected. There is not convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. (C) The -value is greater than , and the null hypothesis is not rejected. There is convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. (D) The -value is greater than , and the null hypothesis is rejected. There is convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. (E) The -value is greater than , and the null hypothesis is not rejected. There is not convincing evidence to support the claim that younger voters are more affected by negative ads than are older voters. 235. Which of the following is the best interpretation of the power of a significance test? (A) Power is the probability of detecting an effect if no effect exists. (B) Power is the probability of detecting an effect if an effect exists. (C) Power is the probability of detecting an effect whether or not an effect exists. (D) Power is the probability of not detecting an effect if no effect exists. (E) Power is the probability of not detecting an effect if an effect exists. 236. A fitness center piloted two new programs to help people reduce stress levels and maintain a healthy lifestyle. After one month, 112 of the 125 people who volunteered for a program in mindfulness reported a reduction in stress levels, and 110 of the 135 people who volunteered for a yoga program reported a reduction in stress levels. The fitness center wants to investigate whether there is a significant difference between the proportions of all people in the two programs who would report reductions in stress levels. Have the conditions for inference been met? (A) No, because the samples were not selected or assigned using a random method. (B) No, because the sizes of the samples are too large compared to the size of the population. (C) No, because the normality of the sampling distribution cannot be assumed; the number of people who experienced stress relief is not large enough. (D) No, because the normality of the sampling distribution cannot be assumed; the number of people who did not experience stress relief is not large enough. (E) Yes, because all conditions for making statistical inference have been met. Page 86 of 86 AP Statistics