Statistics Exam 2020

Section I: Multiple-Choice 1. Which of the following histograms has a shape that is approximately uniform? (A) (B) (C) (D) (E) 2020 2. A recent study reported that 45 percent of adults in the United States now get all their news online. A random sample of 8 adults in the United States will be selected. What is the probability that 6 of the selected adults get all their news online? 6 8 2 (A)    0.45   0.55  2   6 6 2 (B)    0.45   0.55  2 8 2 8 (C)    0.45   0.55  6 8 6 2 (D)    0.45   0.55  6   3. 8 8 6 (E)    0.45   0.55  6 In 2011, 17 percent of a random sample of 200 adults in the United States indicated that they consumed at least 3 pounds of bacon that year. In 2016, 25 percent of a random sample of 600 adults in the United States indicated that they consumed at least 3 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 3 pounds of bacon in 2016 is different from that of 2011? (A) z  0.17  0.25  0.17  0.83   0.25 0.75 200 (B) z  600 0.17  0.25  0.17  0.83   0.25 0.75 600 (C) z  (D) z  (E) z  200 0.17  0.25 1 1  0.21 0.79   200  600   0.17  0.25 1  1  0.23 0.77   200  600   0.17  0.25 1  1  0.50  0.50   200  600    2020 4. In a recent year, the distribution of age for senators in the United States Senate was unimodal and roughly symmetric with mean 65 years and standard deviation 10.6 years. Consider a simulation with 200 trials in which, for each trial, a random sample of 5 senators’ ages is selected and the mean age calculated. Which of the following best describes the distribution of the 200 sample mean ages? (A) Approximately normal with mean 65 years and standard deviation 10.6 years (B) Approximately normal with mean 65 years and standard deviation 10.6 years 5 (C) Approximately normal with mean 65 years and standard deviation 10.6 years 200 (D) Approximately uniform with mean 65 years and standard deviation 10.6 years 5 (E) Approximately uniform with mean 65 years and standard deviation 10.6 years 200 5. An athletic director believes that more than 50 percent of the students in a certain school district exercise at least 3.5 hours per week. To investigate the belief, the director selected a random sample of 40 students in the school district and found that 60 percent of the students in the sample exercise at least 3.5 hours per week. Let p represent the proportion of all students in the school district who exercise at least 3.5 hours per week. Which of the following is the most appropriate alternative hypothesis to test the director’s claim? (A) Ha : p  0.5 (B) Ha : p  0.5 (C) Ha : p  0.5 (D) Ha : p  0.6 (E) Ha : p  0.6 6. For a certain population of penguins, the distribution of weight is approximately normal with mean 15.1 kilograms (kg) and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight between 13.0 kg and 16.5 kg? (A) 17% (B) 34% (C) 57% (D) 68% (E) 74% 2020 7. A researcher collected data on the latitude, in degrees north of the equator, and the average low temperature, in degrees Fahrenheit, for a random sample of cities in Europe. The data were used to create the following equation for the least-squares regression line. predicted average low temperature  65.5  0.70  latitude  Which of the following is the best interpretation of the slope of the line? (A) For each one degree north of the equator increase, the predicted average low temperature increases on average by 0.70 degree Fahrenheit. (B) For each one degree north of the equator increase, the predicted average low temperature decreases on average by 0.70 degree Fahrenheit. (C) For each 0.7 degree north of the equator increase, the predicted average low temperature decreases on average by 1 degree Fahrenheit. (D) For each one degree Fahrenheit increase in average low temperature, the predicted latitude increases on average by 0.70 degree north of the equator. (E) For each one degree Fahrenheit increase in average low temperature, the predicted latitude decreases on average by 0.70 degree north of the equator. 8. An independent polling agency was hired to track the preferences of registered voters in a district for an upcoming election. The polling agency divided the district into twenty regions and believes that the regions are similar to one another in their composition. The agency then randomly selected two of the regions and surveyed all registered voters in both regions. Which of the following best describes the sampling method used by the polling agency? (A) Convenience sampling (B) Simple random sampling (C) Stratified random sampling (D) Systematic sampling (E) Cluster sampling 9. A sports physician conducted a study to investigate whether there is an association between running experience and the occurrence of a certain sport injury for marathon runners while training for a marathon. Data were collected on a random sample of 51 marathon runners. Each runner from the sample was categorized by running experience (low, medium, high) and whether or not the runner experienced the sport injury while training for a marathon. The conditions 2 for inference were met, and a c test statistic of approximately 8.12 was calculated. Which of the following describes the p-value of the test? (A) p-value  0.25 (B) 0.10  p-value  0.25 (C) 0.05  p-value  0.10 (D) 0.01  p-value  0.05 (E) p-value  0.01 2020 10. An agricultural engineer selected a random sample of 30 farms in the United States to construct a 95 percent confidence interval for the mean size, in acres, of farms in the United States. The resulting interval was (367, 558). Which of the following is an appropriate interpretation of the 95 percent confidence level? (A) Approximately 95% of the farm sizes in the sample are between 367 acres and 558 acres. (B) Approximately 95% of all farm sizes in the United States are between 367 acres and 558 acres. (C) Approximately 95% of all random samples of size 30 from the population will have a mean farm size between 367 acres and 558 acres. (D) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the mean size of farms in the United States. (E) Approximately 95% of all random samples of size 30 from the population will produce intervals that contain the sample mean. 11. An experiment was designed to investigate the relationship between the dosage of a certain migraine medication and the amount of time until relief from the headache was experienced. Four dosages in milligrams (mg)—2.5, 5.0, 7.5, and 10—of the medication were used. The 20 participants in the experiment were known to experience migraines. Each participant was randomly assigned one of the four dosages. When the participants experienced a migraine, they took the assigned medication and recorded the number of minutes it took to experience relief from the headache. The mean number of minutes it took each group to experience relief was compared. What were the experimental units in the experiment? (A) The number of minutes to experience relief (B) The mean number of minutes it took each group to experience relief (C) The four dosages (D) The 20 participants (E) The relationship between the dosage and the amount of time 12. The recommended dietary allowance of iron for women under the age of 51 is 18 milligrams (mg) per day. A medical researcher studying women living in a certain region suspected that the women were getting less than the daily allowance of iron, on average. The researcher took a random sample of women under the age of 51 from the region and measured their daily iron intakes. The following hypotheses were tested at the significance level of   0.05 for the population mean u of the daily iron intake for women in the region. H0 :   18 Ha :   18 2020 All conditions for inference were met, and the resulting p-value was 0.031. Which of the following is an appropriate conclusion? (A) The p-value is less than α, and the null hypothesis should be rejected. There is convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg. (B) The p-value is less than α, and the null hypothesis should be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg. (C) The p-value is less than α, and the null hypothesis should not be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg. (D) The p-value is greater than α, and the null hypothesis should be rejected. There is convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg. (E) The p-value is greater than α, and the null hypothesis should not be rejected. There is not convincing statistical evidence that the mean daily intake of iron for women in the region is less than the recommended 18 mg. 13. At a small company, 40 percent of the employees are classified as junior level, and 32 percent of the employees work in department A. Of those classified as junior level, 55 percent work in department A. One employee will be selected at random. What is the probability that the selected employee works in department A and is not classified as junior level? (A) 0.10 (B) 0.19 (C) 0.22 (D) 0.32 (E) 0.50 14. A one-sample z-test for a proportion at the significance level of   0.10 will be conducted for the following set of hypotheses. H0 : p  0.50 Ha : p  0.50 For which of the following is the probability of a Type II error the greatest? (A) A sample size of 200 and a true proportion of 0.45 (B) A sample size of 200 and a true proportion of 0.40 (C) A sample size of 200 and a true proportion of 0.35 (D) A sample size of 100 and a true proportion of 0.45 (E) A sample size of 100 and a true proportion of 0.35 2020 15. A small-business owner collected data from a random sample on the amount spent on an order and the time it takes to fill the order. The resulting data were used to complete a linear regression analysis of time, in minutes, versus amount spent, in dollars, and to create the following residual plot. Based on the residual plot, which condition for inference for the slope of the regression line does not appear to be satisfied? (A) The true relationship between the number of items and the amount spent on an order is linear. (B) For each amount spent on an order, the distribution of time to fill the order is approximately normal. (C) The standard deviation of the distribution of time to fill an order is the same for each amount spent on the order. (D) The data are collected using a random sample or randomized experiment. (E) The sample size is less than 10% of the population size. 2020 16. An athletic trainer wanted to investigate the relationship between an athlete’s resting heart rate and the heart rate after exercise. From a sample of 12 athletes, the athletic trainer recorded each athlete’s resting heart rate, in beats per minute, and heart rate, in beats per minute, after 5 minutes of moderate exercise. The results of a regression analysis of the data are shown in the following computer output. Predictor Constant Resting Heart Rate S = 9.9702 Coef 17.5 1.786 SE Coef 29.2 0.453 T 0.60 3.94 P 0.563 0.003 R-Sq = 60.88% Assume the conditions for inference are met. Which of the following represents a 95 percent confidence for the slope of the population regression line? (A) 17.5 ± 1.96 ( 29.2 ) (B) 1.786 ± 1.96 ( 0.453 )  0.453  (C) 1.786 ± 1.96    12   0.453  (D) 1.786 ± 2.228    12  (E) 1.786 ± 2.228 ( 0.453 ) 2020