9-3 Matched Pairs 479 14. Heights of Fathers and Sons Listed below are heights (in.) of fathers and their first sons. The data are from a journal kept by Francis Galton. (See Data Set 10 “Family Heights” in Appendix B.) Use a 0.05 significance level to test the claim that there is no difference in heights between fathers and their first sons. Height of Father 72.0 66.0 69.0 70.0 70.0 70.0 70.0 75.0 68.2 65.0 Height of Son 73.0 68.0 68.0 71.0 70.0 70.0 71.0 71.0 70.0 63.0 15. Hypnotism for Reducing Pain A study was conducted to investigate the effectiveness of hypnotism in reducing pain. Results for randomly selected subjects are given in the accompanying table (based on “An Analysis of Factors That Contribute to the Efficacy of Hypnotic Analgesia,” by Price and Barber, Journal of Abnormal Psychology, Vol. 96, No. 1). The values are before and after hypnosis; the measurements are in centimeters on a pain scale. Higher values correspond to greater levels of pain. Construct a 95% confidence interval for the mean of the “before>after” differences. Does hypnotism appear to be effective in reducing pain? Subject A B C D E F G H Before 6.6 6.5 9.0 10.3 11.3 8.1 6.3 11.6 After 6.8 2.4 7.4 8.5 8.1 6.1 3.4 2.0 16. Gosset Data Listed below are paired data from W. S. Gosset, who introduced us to the famous t distribution. The values are hours of sleep gained or lost by 10 patients after each of two different sleep treatments (based on data from “Probable Error of the Mean,” by W. S. Gosset, Biometrica, Vol. 6). a. Use a 0.01 significance level to test the claim that both sleep treatments have the same effect. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? Dextro 0.7 -1.6 -0.2 -1.2 -1.0 3.4 3.7 0.8 0.0 2.0 Laevo 1.9 0.8 1.1 0.1 -0.1 4.4 5.5 1.6 4.6 3.4 Larger Data Sets. In Exercises 17–24, use the indicated Data Sets from Appendix B. The complete data sets can be found at www.TriolaStats.com. Assume that the paired sample data are simple random samples and the differences have a distribution that is approximately normal. 17. Measured and Reported Weights Repeat Exercise 5 using all of the 2971 measured and reported weights (lb) of females listed in Data Set 4 “Measured and Reported” in Appendix B. Did the larger data set have much of an effect on the results? 18. Measured and Reported Weights Repeat Example 1 using all of the 2784 measured and reported weights of males listed in Data Set 4 “Measured and Reported” in Appendix B. Did the larger data set have much of an effect on the results? 19. Oscars Repeat Exercise 11 “Oscars” using all of the sample data from Data Set 21 “Oscar Winner Age” in Appendix B. Note that the pairs of data consist of ages that are matched according to the year in which the Oscars were won. Again use a significance level of 0.05. 20. Heights of Presidents Repeat Exercise 12 “Heights of Presidents” using all of the sample data from Data Set 22 “Presidents” in Appendix B.
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