546 CHAPTER 10 Chi-Square Tests and the F -Distribution 25. Use the contingency table and expected frequencies from Exercise 9. At a = 0.05, test the hypothesis that the variables are dependent. 26. Use the contingency table and expected frequencies from Exercise 10. At a = 0.01, test the hypothesis that the variables are dependent. 27. Use the contingency table and expected frequencies from Exercise 11. At a = 0.10, test the hypothesis that the variables are independent. 28. Use the contingency table and expected frequencies from Exercise 12. At a = 0.10, test the hypothesis that the variables are dependent. Extending Concepts Homogeneity of Proportions Test In Exercises 29–32, use this information about the homogeneity of proportions test. Another chi-square test that involves a contingency table is the homogeneity of proportions test. This test is used to determine whether several proportions are equal when samples are taken from different populations. Before the populations are sampled and the contingency table is made, the sample sizes are determined. After randomly sampling different populations, you can test whether the proportion of elements in a category is the same for each population using the same guidelines as the chi-square independence test. The null and alternative hypotheses are always some variation of these statements. H0: The proportions are equal. Ha: At least one of the proportions is different from the others. Performing a homogeneity of proportions test requires that the observed frequencies be obtained using a random sample, and each expected frequency must be greater than or equal to 5. 29. Motor Vehicle Crash Deaths The contingency table shows the results of a random sample of motor vehicle crash deaths by age and gender. At a = 0.05, perform a homogeneity of proportions test on the claim that the proportions of motor vehicle crash deaths involving males or females are the same for each age group. (Adapted from Insurance Institute for Highway Safety) Age Gender 16 –24 25 –34 35 – 44 45 –54 Male 80 97 76 73 Female 33 35 26 27 Age Gender 55–64 65–74 75–84 85 and older Male 81 51 30 12 Female 26 23 19 9 30. Obsessive-Compulsive Disorder The contingency table at the left shows the results of a random sample of patients with obsessive-compulsive disorder after being treated with a drug or with a placebo. At a = 0.10, perform a homogeneity of proportions test on the claim that the proportions of the results for drug and placebo treatments are the same. (Adapted from The Journal of the American Medical Association) Treatment Result Drug Placebo Improvement 39 25 No change 54 70 TABLE FOR EXERCISE 30
RkJQdWJsaXNoZXIy NjM5ODQ=