498 CHAPTER 9 Inferences from Two Samples Two Means. In Exercises 9–12, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-2. Compare the results to those obtained in the original exercise. 9.Exercise 17 in Section 9-2 “Are Weights Changing Over Time?” 10. Exercise 18 in Section 9-2 “Queues” 11.Exercise 19 in Section 9-2 “Regular Coke and Diet Coke” 12.Exercise 20 in Section 9-2 “Blanking Out on Tests” (use randomization only.) Matched Pairs. In Exercises 13–16, use (a) randomization and (b) bootstrapping for the indicated exercise from Section 9-3. Compare the results to those obtained in the original exercise. 13.Exercise 5 in Section 9-3 “Measured and Reported Weights” 14.Exercise 6 in Section 9-3 “Do Men Talk Less than Women?” 15.Exercise 7 in Section 9-3 “The Freshman 15” 16.Exercise 8 in Section 9-3 “QWERTY vs Dvorak” 17.Effect of the Number of Bootstrap Samples Use the weights (lb) of regular Coke and diet Coke from Data Set 37 “Cola Weights and Volumes.” Use resampling to find a 95% confidence interval estimate of the difference between the two population means. Use 1000 bootstrap samples, then use 10,000 resamples. Does the larger number of resamples have much of an effect on the results? 18.Bootstrapping with Two Standard Deviations Use the weights (lb) of regular Coke and diet Coke from Data Set 37 “Cola Weights and Volumes.” Use bootstrap resamples to construct a 95% confidence interval estimate of the ratio of the two variances. What does the confidence interval suggest about the variation in the two populations? 9-5 Beyond the Basics 1.Identifying Hypotheses In a randomized clinical trial of adults with an acute sore throat, 288 were treated with the drug dexamethasone and 102 of them experienced complete resolution; 277 were treated with a placebo and 75 of them experienced complete resolution (based on data from “Effect of Oral Dexamethasone Without Immediate Antibiotics vs Placebo on Acute Sore Throat in Adults,” by Hayward et al., Journal of the American Medical Association). Identify the null and alternative hypotheses corresponding to the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution. 2.Test Values Find the values of pn 1, p n 2, and the pooled proportion p obtained when testing the claim given in Exercise 1. 3. P-Value The test statistic of z = 2.14 is obtained when using the data from Exercise 1 and testing the claim that patients treated with dexamethasone and patients given a placebo have the same rate of complete resolution. a. Find the P-value for the test. b. If a significance level of 0.05 is used to test the claim, what should be concluded? Chapter Quick Quiz
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