450 CHAPTER 9 Inferences from Two Samples 4. Using Confidence Intervals a. In general, when dealing with inferences about two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method? b. If we want to use a 0.05 significance level to test the claim that p1 6 p2 using a confidence interval, what confidence level should we use for that confidence interval? c. If we test the claim in part (b) using the sample data in Exercise 1, we get this confidence interval: -0.000508 6 p1 - p2 6 - 0.000309. What does this confidence interval suggest about the claim? Interpreting Displays. In Exercises 5 and 6, use the results from the given displays. 5. Testing Laboratory Gloves The New York Times published an article about a study in which Professor Denise Korniewicz and other Johns Hopkins researchers subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses. Among 240 latex gloves, 7% leaked viruses. See the accompanying display of the Statdisk results. Using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. 6. Treating Carpal Tunnel Syndrome Carpal tunnel syndrome is a common wrist complaint resulting from a compressed nerve, and it is often the result of extended use of repetitive wrist movements, such as those associated with the use of a keyboard. In a randomized controlled trial, 73 patients were treated with surgery and 67 were found to have successful treatments. Among 83 patients treated with splints, 60 were found to have successful treatments (based on data from “Splinting vs Surgery in the Treatment of Carpal Tunnel Syndrome,” by Gerritsen et al., Journal of the American Medical Association, Vol. 288, No. 10). Use the accompanying StatCrunch display with a 0.01 significance level to test the claim that the success rate is better with surgery. Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. 7. Buttered Toast Drop Test The Discovery TV show MythBusters conducted an experiment in which they tested the common belief that dropped buttered toast tends to fall with the buttered side down. Here are the results of that experiment: Among 48 slices of buttered toast that were dropped, 19 landed with the buttered side down. Among 48 slices of toast that were not buttered but were marked with an X on one side, 22 landed with the X side down. Use a 0.05 significance level to test the claim that when dropped, buttered toast and toast marked with an X have the same proportion that land with the buttered>X side down. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. 8. Tennis Challenges Since the Hawk-Eye instant replay system for tennis was introduced at the U.S. Open in 2006, men’s singles players challenged 6036 referee calls, with the result that 1757 were successfully overturned. Women’s singles players challenged 3327 referee calls, with the result that 887 were successfully overturned. Use a 0.05 significance level to test the claim that men and women singles players have equal success in challenging calls. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. c. Based on the results, does it appear that men and women have equal success in challenging calls? 9. Cell Phones and Handedness A study was conducted to investigate the association between cell phone use and hemispheric brain dominance. Among 216 subjects who prefer to use their left ear for cell phones, 166 were right-handed. Among 452 subjects who prefer to use their right ear for cell phones, 436 were right-handed (based on data from “Hemispheric Statdisk StatCrunch
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