CHAPTER 11 Review Exercises 605 9. Find the number of degrees of freedom. 10. Given that the P-value for the hypothesis test is 0.000 when rounded to three decimal places, what do you conclude? What do the results indicate about the rule that women and children should be the first to be saved? Review Exercises 1.Weather-Related Deaths For the most recent year as of this writing, the numbers of weather-related U.S. deaths for each month were 61, 14, 22, 26, 29, 42, 93, 49, 47, 35, 96, 16, listed in order beginning with January (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Provide an explanation for the result. 2.Benford and Cheating in Badminton According to Benford’s law, for many data sets the leading digits of individual sample values follow the distribution shown in the first two rows of the following table. In normal and fair badminton play, leading digits in the numbers of rallies tend to follow the distribution of Benford’s law. In a study of leading digits for the numbers of badminton rallies in international tournaments, the frequencies in the bottom row of the table were obtained (based on data from “Preliminary Study to Detect Match-Fixing: Benford’s Law in Badminton Rally Data,” by Park et al., Journal of Physical Education and Sports Management, Vol. 3, No. 1). Does it appear that the observed frequencies fit the distribution from Benford’s law? What does the result suggest about cheating in those matches? Leading Digit 1 2 3 4 5 6 7 8 9 Benford’s Law: Distribution of Leading Digits 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Leading Digits of Numbers of Rallies 3679 1515 974 898 866 757 740 743 649 3.Splint or Surgery? A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below (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). The results are based on evaluations made one year after the treatment. Using a 0.01 significance level, test the claim that success is independent of the type of treatment. What do the results suggest about treating carpal tunnel syndrome? Successful Treatment Unsuccessful Treatment Splint Treatment 60 23 Surgery Treatment 67 6 4.Does the Treatment Affect Success? The following table lists frequencies of successes and failures for different treatments used for a stress fracture in a foot bone (based on data from “Surgery Unfounded for Tarsal Navicular Stress Fracture,” by Bruce Jancin, Internal Medicine News, Vol. 42, No. 14). Use a 0.05 significance level to test the claim that success of the treatment is independent of the type of treatment. What does the result indicate about the increasing trend to use surgery? Success Failure Surgery 54 12 Weight-Bearing Cast 41 51 Non–Weight-Bearing Cast for 6 Weeks 70 3 Non–Weight-Bearing Cast for Less Than 6 Weeks 17 5
RkJQdWJsaXNoZXIy NjM5ODQ=