466 CHAPTER 9 Inferences from Two Samples 10. Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Higher scores correspond to more creativity. The researchers make the claim that “blue enhances performance on a creative task.” a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. b. Construct the confidence interval appropriate for the hypothesis test in part (a). What is it about the confidence interval that causes us to reach the same conclusion from part (a)? Red Background: n = 35, x = 3.39, s = 0.97 Blue Background: n = 36, x = 3.97, s = 0.63 11. Magnet Treatment of Pain People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results given below are among the results obtained in the study (based on data from “Bipolar Permanent Magnets for the Treatment of Chronic Lower Back Pain: A Pilot Study,” by Collacott, Zimmerman, White, and Rindone, Journal of the American Medical Association, Vol. 283, No. 10). Higher scores correspond to greater pain levels. a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo). b. Construct the confidence interval appropriate for the hypothesis test in part (a). c. Does it appear that magnets are effective in treating back pain? Is it valid to argue that magnets might appear to be effective if the sample sizes are larger? Reduction in Pain Level After Magnet Treatment: n = 20, x = 0.49, s = 0.96 Reduction in Pain Level After Sham Treatment: n = 20, x = 0.44, s = 1.4 12. Second-Hand Smoke Samples from Data Set 15 “Passive and Active Smoke” in Appendix B include cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, x = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, x = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. a. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. b. Construct the confidence interval appropriate for the hypothesis test in part (a). c. What do you conclude about the effects of second-hand smoke? 13. Bicycle Commuting A researcher used two different bicycles to commute to work. One bicycle was steel and weighed 30.0 lb; the other was carbon and weighed 20.9 lb. The commuting times (minutes) were recorded with the results shown below (based on data from “Bicycle Weights and Commuting Time,” by Jeremy Groves, British Medical Journal). a. Use a 0.05 significance level to test the claim that the mean commuting time with the heavier bicycle is the same as the mean commuting time with the lighter bicycle. b. Construct the confidence interval suitable for testing the claim in part (a). Heavier Bicycle: n = 30, x = 107.8 min, s = 4.9 min Lighter Bicycle: n = 26, x = 108.4 min, s = 6.3 min
RkJQdWJsaXNoZXIy NjM5ODQ=