Review Exercises 459 Section 8.4 In Exercises 25–28, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance a. Assume the samples are random and independent. 25. Claim: p1 = p2; a = 0.05 Sample statistics: x1 = 425, n1 = 840 and x2 = 410, n2 = 760 26. Claim: p1 … p2; a = 0.01 Sample statistics: x1 = 36, n1 = 100 and x2 = 46, n2 = 200 27. Claim: p1 7 p2; a = 0.10 Sample statistics: x1 = 261, n1 = 556 and x2 = 207, n2 = 483 28. Claim: p1 6 p2; a = 0.05 Sample statistics: x1 = 86, n1 = 900 and x2 = 107, n2 = 1200 In Exercises 29 and 30, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent. 29. A medical research team conducted a study to test the effect of a drug used to treat a type of inflammation. In the study, 68 subjects took the drug and 68 subjects took a placebo. The results are shown below. At a = 0.05, can you reject the claim that the proportion of subjects who had at least 24 weeks of accrued remission is the same for the two groups? (Source: The New England Journal of Medicine) Drug Placebo Yes 2 Do You Have At Least 24 Weeks of Accrued Remission? Yes 19 No 49 No 66 30. A traffic safety research team conducted a survey over two years on the use of motorcycle helmets. In the survey, motorcyclists in states where helmet use is required were asked whether they use helmets that are compliant with federal safety regulations. In 2019, 389 motorcyclists were surveyed and in 2020, 338 motorcyclists were surveyed. The results are shown below. At a = 0.01, can you support the claim that the proportion of motorcyclists in states where helmet use is required who use such helmets decreased from 2019 to 2020? (Adapted from National Highway Traffic Safety Administration) 2019 2020 Do You Use Helmets That Are Compliant with Federal Safety Regulations? No 10.8% Yes 89.2% No 16.0% Yes 84.0%
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