574 CHAPTER 10 Chi-Square Tests and the F -Distribution 8. The contingency table shows the distribution of a random sample of fatal pedestrian and bicyclist motor vehicle collisions by time of day in a recent year. At a = 0.10, can you conclude that the type of crash victim and the time of day are related? (Adapted from National Highway Traffic Safety Administration) Time of day Victim 12 – 5:59 A.M. 6 – 11:59 A.M. 12 – 5:59 P.M. 6 – 11:59 P.M. Pedestrian 924 581 617 2054 Bicyclist 72 124 145 213 Section 10.3 In Exercises 9 –12, find the critical F-value for a right-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D. 9. a = 0.05, d.f.N = 6, d.f.D = 50 10. a = 0.01, d.f.N = 12, d.f.D = 10 11. a = 0.10, d.f.N = 5, d.f.D = 12 12. a = 0.05, d.f.N = 20, d.f.D = 25 In Exercises 13 –16, find the critical F-value for a two-tailed test using the level of significance a and degrees of freedom d.f.N and d.f.D. 13. a = 0.10, d.f.N = 15, d.f.D = 27 14. a = 0.05, d.f.N = 9, d.f.D = 8 15. a = 0.01, d.f.N = 40, d.f.D = 60 16. a = 0.01, d.f.N = 11, d.f.D = 13 In Exercises 17–20, (a) identify the claim and state H0 and Ha, (b) find the critical value and identify the rejection region, (c) find the test statistic F, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. 17. A travel consultant claims that the standard deviations of hotel room rates for Sacramento, CA, and San Francisco, CA, are the same. A sample of 36 hotel room rates in Sacramento has a standard deviation of $51 and a sample of 31 hotel room rates in San Francisco has a standard deviation of $37. At a = 0.10, can you reject the travel consultant’s claim? (Adapted from Expedia) 18. An agricultural analyst is comparing the wheat production in Oklahoma counties. The analyst claims that the variation in wheat production is greater in Garfield County than in Kay County. A sample of 21 Garfield County farms has a standard deviation of 0.76 bushel per acre. A sample of 16 Kay County farms has a standard deviation of 0.58 bushel per acre. At a = 0.10, can you support the analyst’s claim? (Adapted from Environmental Verification and Analysis Center—University of Oklahoma) 19. An instructor claims that the variance of SAT evidence-based reading and writing scores is different than the variance of SAT math scores. The table shows the SAT evidence-based reading and writing scores for 12 randomly selected students and the SAT math scores for 12 randomly selected students. At a = 0.01, can you support the instructor’s claim? Reading and writing Math 480 600 560 310 610 800 680 730 340 540 360 740 630 750 530 520 520 650 380 560 690 630 460 400
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