Statistics Exam Solutions

SOLUTIONS 1. Which of the following is a key distinction between well designed experiments and observational studies? (A) More subjects are available for experiments than for observational studies. (B) Ethical constraints prevent large-scale observational studies. Experiments are less costly to conduct than observational studies. yes (D) An experiment can show a direct cause and effect relationship, whereas an observational study cannot. (E) Tests of significance cannot be used on data collected from an observational study. 2. A manufacturer of balloons claims that p, the proportion of its balloons that burst when inflated to a diameter of up to 12 inches, is no more than 0.05. Some customers have complained that the balloons are bursting more frequently. If the customers want to conduct an experiment to test the manufacturer's claim, which of the following fhypotheses would be appropriate? 50 prop 7.05 (A) Ho: p 0.05, H₂: p = 0.05 B (B) Ho: p = 0.05, H₂: p > 0.05 (C) Ho: p = 0.05, H₂: p≠ 0.05 (D) Ho: p = 0.05, H₂: p < 0.05 (E) Ho: p<0.05, H₂: p = 0.05 3. Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class? Ist exam 2nd exam 7=1 (A) She scored much better on the first exam. (B) She scored much better on the second exam. (C) She scored about equally well on both exams. findz-scores (D) It is impossible to tell because the class size is not given. (E) It is impossible to tell because the correlation between the two sets of exam scores is not given. 3/10 4. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches the shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscriber's behavior in this simulation? A (A) Assign "0, 1, 2" as watching the shopping channel at least once a week and "3, 4, 5, 6, 7, 8, and 9" as not watching. 3 choices Ichokes (B) Assign "0, 1, 1, 2, 2, 3" as watching the shopping channel at least once a week and "4, 5, 6, 6, 7, 8, and 9" as not watching. (C) Assign "1, 2, 3, 4, 5" as watching the shopping channel at least once a week and "6, 7, 8, 9, and 0" as not watching. (D) Assign "0" as watching the shopping channel at least once a week and "1, 2, 3, 4, and 5" as not watching; ignore digits "6, 7, 8, and 9." (E) Assign "3" as watching the shopping channel at least once a week and "0, 1, 2, 4, 5, 6, 7, 8, and 9" as not watching. STAT EXAM 40 MULTIPLE CHOICE 90 MINUTES 5. The number of sweatshirts a vendor sells daily has the following probability distribution. Number of Sweatshirts x 0 1 0.3 0.2 2 0.3 3 4 5 0.1 0.08 0.02 If each sweatshirt sells for $25, what is the expected daily total dollar amount taken in by the vendor from the sale of sweatshirts? (A) $5.00 (B) $7.60 (C) $35.50 (D) $38.00 (E) $75.00 Sigma x,p(x)= i(0.2) + 2(0.3) + 3(0.1) + 4(0.08) +5(,02)= 1.52 x25 6. The correlation between two scores X and Y equals 0.8. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be (A) -0.8 (B) -0.2 (C) 0.0 (D) 0.2 (E) 0.8 Stays ame transformations don't change correlation 7. Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? Mean Standard Deviation +4 each score (A) 51 14 (B) 51 18 (C) AT S stays S same... only a shift of data, no change in spread, 14 (D) 47 16 (E) 42 18 8. A test engineer wants to estimate the mean gas mileage µ (in miles per gallon) for a particular model of automobile. Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car. A dotplot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean and standard deviation of these values are 25.5 and 3.01, respectively. Assuming that these 11 automobiles can be con-sidered a simple random sample of cars of this model, which of the following is a correct statement? (A) A 98% confidence interval for µ is googlelongdiv x * 25 plus/minus 2.228 * 301/(sqrt(11)) ^ 5 (B) A 95% confidence interval for µ is 25.5 plus/minus 2.201 * 3.01/(sqrt(11)) df = 10 uset-chart 95010 (C) A 95% confidence interval for u is 25.5 plus/minus 2.228 * 3.01/(sqrt(10)) (D) A 95% confidence interval for µ is 25.5 plus/minus 2.201 * 3.01/(sqrt(10)) (E) The results cannot be trusted; the sample is too small. P.2 A P(x) 38. Suppose that public opinion in a large city is 65 percent in favor of increasing taxes to support the public school system and 35 percent against such an increase. If a random sample of 500 people from this city are interviewed, what is the approximate probability that more than 200 of these people will be against increasing taxes? (A) * binomial(500,200) * (0.65) ^ 200 * (0.35) ^ 300 200 (B) binomial(500,200) * (0.35) ^ 200 * (0.65) ^ 300 exoetty 200 ECOP (C) p( z > (0.6 - 0.65)/(sqrt(((0.65)(35))/500)) k[ z > (0.4 - 0.35)/(sqrt(((0.4)(0.6))/500)) (E) z> 0.40-0.35 sqrt (35)(0.65) 5(00 ) mu_{x} = 0.35 p = 200/500 = 0.4 sigma_{x} = sqrt((p(1 - rho))/n) stdev basedon what you believe. 3570 againt 39. As lab partners, Sally and Betty collected data for a significance test. Both calculated the same z-test statistic, but Sally found the results were significant at the alpha = 0.05 level while Betty found that the results were not. When checking their results, the women found that the only difference in their work was that Sally had used a two-sided test, while Betty used a one-sided test. Which of the following could have been their test statistic? ?? A (A)-1.980 (A) (B) -1.690 (C) 1.340 (D) 1.690 (E) 1.780 Sally 2-sided significant at a=.05 Betty 1-sided not signif 40. A student working on a history project decided to find a 95 percent confidence interval for the difference in mean age at the time of election to office for former American Presidents versus former British Prime Ministers. The student found the ages at the time of election to office for the members of both groups, which included all of the American Presidents and all of the British Prime Ministers, and used a calculator to find the 95 percent confidence interval based on the 1-distribution. This procedure is not appropriate in this context because (A) the sample sizes for the two groups are not equal B (B) the entire population was measured in both cases, so the actual difference in means can be computed and a confidence interval should not be used You know the actual difference No need tomate (C) elections to office take place at different intervals in the two countries, so the distribution of ages cannot be the same (D) ages at the time of election to office are likely to be skewed rather than beli-shaped, so the assumptions for using this confidence interval formula are not valid (E) ages at the time of election to office are likely to have a few large outliers, so the assumptions for using this confidence interval formula are not valid