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NAME_________________________ DATE: ______________________ AP/ACC Statistics Unit 5 AP Test ReviewβMultiple Choice Choose the response that best answers the question or completes the statement. 1. Which of the following is an incorrect statement? (A) The sampling distribution of π₯Μ has mean equal to the population mean π even if the population is not normally distributed. (B) The sampling distribution of π₯Μ has standard deviation π even if the population is not normally distributed. βπ (C) The sampling distribution of π₯Μ is normal if the population has a normal distribution. (D) When n is large, the sampling distribution of π₯Μ is approximately normal even if the population is not normally distributed. (E) The larger the value of the sample size n, the closer the standard deviation of the sampling distribution of π₯Μ is to the standard deviation of the population. 2. Which of the following is a true statement? (A) The sampling distribution of πΜ has a mean equal to the population proportion π. (B) The sampling distribution of πΜ has a standard deviation (B) The mean gets closer to the population mean, the standard deviation becomes smaller, and the shape becomes more skewed left. (C) The mean gets closer to the population mean, the standard deviation stays the same, and the shape becomes closer to normal. (D) The mean gets closer to the population mean, the standard deviation becomes smaller, and the shape becomes closer to normal. (E) The mean stays the same, the standard deviation becomes smaller, and the shape becomes closer to normal. 5. Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts an SRS of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary? (A) .1469 (B) .1977 (C) .4207 (D) .8023 (E) .8531 equal to βππ(1 β π). (C) The sampling distribution of πΜ has a standard deviation which becomes larger as the sample size becomes larger. (D) The sampling distribution of πΜ is considered close to normal provided that π > 30. (E) The sampling distribution of πΜ is always close to normal. 6. The average outstanding bill for delinquent customer accounts for a national department store chain is $187.50 with a standard deviation of $54.50. In a simple random sample of 50 delinquent accounts, what is the probability that the mean outstanding bill is over $200? (A) .0526 (B) .0667 (C) .4090 (D) .5910 (E) .9474 3. In a school of 2500 students, the students in an AP Statistics class are planning a random survey of 100 students to estimate the proportion who would rather drop lacrosse rather than band during this time of severe budget cuts. Their teacher suggests instead to survey 200 students in order to (A) reduce bias. (B) reduce variability. (C) increase bias. (D) increase variability. (E) make possible stratification between lacrosse and band. 7. Changing from a 95% confidence interval estimate for a population proportion to a 99% confidence interval estimate, with all other things being equal, (A) increases the interval size by 4%. (B) decreases the interval size by 4%. (C) increases the interval size by 31%. (D) decreases the interval size by 31%. (E) This question cannot be answered without knowing the sample size. 4. The ages of people who died last year in the United States is skewed left. What happens to the sampling distribution of sample means as the sample size goes from π = 50 to π = 200? (A) The mean gets closer to the population mean, the standard deviation stays the same, and the shape becomes more skewed left. 8. A confidence interval estimate is determined from the GPAs of a simple random sample of n students. All other things being equal, which of the following will result in a smaller margin of error? (A) A smaller confidence level (B) A larger sample standard deviation (C) A smaller sample size (D) A larger population size (E) A smaller sample mean 9. A survey was conducted to determine the percentage of high school students who planned to go to college. The results were stated as 82% with a margin of error of ±5%. What is meant by ±5%? (A) Five percent of the population were not surveyed. (B) In the sample, the percentage of students who plan to go to college was between 77% and 87%. (C) The percentage of the entire population of students who plan to go to college is between 77% and 87%. (D) It is unlikely that the given sample proportion result would be obtained unless the true percentage was between 77% and 87%. (E) Between 77% and 87% of the population were surveyed. 10. Most recent tests and calculations estimate at the 95% confidence level that the maternal ancestor to all living humans called mitochondrial Eve lived 273,000 ± 177,000 years ago. What is meant by "95% confidence" in this context? (A) A confidence interval of the true age of mitochondrial Eve has been calculated using z-scores of ±1.96. (B) A confidence interval of the true age of mitochondrial Eve has been calculated using t-scores consistent with df = n - 1 and tail probabilities of ±.025. (C) There is a .95 probability that mitochondrial Eve lived between 96,000 and 450,000 years ago. (D) If 20 random samples of data are obtained by this method, and a 95% confidence interval is calculated from each, then the true age of mitochondrial Eve will be in 19 of these intervals. (E) 95% of all random samples of data obtained by this method will yield intervals that capture the true age of mitochondrial Eve. 11. In a recent Zogby International survey, 11% of 10,000 Americans under 50 said they would be willing to implant a device in their brain to be connected to the Internet if it could be done safely. What is the margin of error at the 99% confidence level? for integration. What size voter sample should be obtained to determine with 90% confidence the support level to within 4%? (A) 21 (B) 25 (C) 423 (D) 600 (E) 1691 13. In a simple random sample of 300 elderly men, 65% were married, while in an independent simple random sample of 400 elderly women, 48% were married. Determine a 99% confidence interval estimate for the difference between the proportions of elderly men and women who are married. 14. Two confidence interval estimates from the same sample are (16.4, 29.8) and (14.3, 31.9). What is the sample mean, and if one estimate is at the 95% level while the other is at the 99% level, which is which? (A) π₯Μ =23.1; (16.4, 29.8) is the 95% level. (B) π₯Μ =23.1; (16.4, 29.8) is the 99% level. (C) It is impossible to completely answer this question without knowing the sample size. (D) It is impossible to completely answer this question without knowing the sample standard deviation. (E) It is impossible to completely answer this question without knowing both the sample size and standard deviation. 15. Nine subjects, 87 to 96 years old, were given 8 weeks of progressive resistance weight training (Journal of the American Medical Association, June 13, 1990, page 3032). Strength before and after training for each individual was measured as maximum weight (in kilograms) lifted by left knee extension: Find a 95% confidence interval estimate for the strength gain. (A) 11.61 ± 3.03 (B) 11.61 ± 3.69 (C) 11.61 ± 3.76 (D) 19.11 ± 1.25 (E) 19.11 ± 3.69 12. A politician wants to know what percentage of the voters support her position on the issue of forced busing 16. You plan to perform a hypothesis test with a level of significance of πΌ = .05. What is the effect on the probability of committing a Type I error if the sample size is increased? (A) The probability of committing a Type I error decreases. (B) The probability of committing a Type I error is unchanged. (C) The probability of committing a Type I error increases. (D) The effect cannot be determined without knowing the relevant standard deviation. (E) The effect cannot be determined without knowing if a Type II error is committed. 17. A research dermatologist believes that cancers of the head and neck will occur most often of the left side, the side next to a window when a person is driving. In a review of 565 cases of head/neck cancers, 305 occurred on the left side. What is the resulting P-value? 18. Suppose you do five independent tests of the form π»0 : π = 38 versus π»π : π > 38, each at the πΌ = .01 significance level. What is the probability of committing a Type I error and incorrectly rejecting a true null hypothesis with at least one of the five tests? (A) .01 (B) .049 (C) .05 (D) .226 (E) .951 19. Suppose π»0 : π = 4, and the power of the test for the alternative hypothesis π = .35 is . 75. Which of the following is a valid conclusion? (A) The probability of committing a Type I error is .05. (B) The probability of committing a Type II error is .65. (C) If the alternative π = .35 is true, the probability of failing to reject π»0 is .25. (D) If the null hypothesis is true, the probability of rejecting it is .25. (E) If the null hypothesis is false, the probability of failing to reject it is .65. 20. A pharmaceutical company claims that 8% or fewer of the patients taking their new statin drug will have a heart attack in a 5-year period. In a government-sponsored study of 2300 patients taking the new drug, 198 have heart attacks in a 5-year period. Is this strong evidence against the company claim? (A) Yes, because the P-value is .005657. (B) Yes, because the P-value is .086087. (C) No, because the P-value is only .005657. (D) No, because the P-value is only .086087. (E) No, because the P-value is over .10.