8.4 EXERCISES SECTION 8.4 Testing the Difference Between Proportions 451 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. What conditions are necessary to use the z@test for testing the difference between two population proportions? 2. Explain how to perform a two-sample z@test for the difference between two population proportions. In Exercises 3–6, determine whether a normal sampling distribution can be used. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance a. Assume the samples are random and independent. 3. Claim: p1 ≠ p2; a = 0.01 Sample statistics: x1 = 35, n1 = 70 and x2 = 36, n2 = 60 4. Claim: p1 6 p2; a = 0.05 Sample statistics: x1 = 471, n1 = 785 and x2 = 372, n2 = 465 5. Claim: p1 = p2; a = 0.10 Sample statistics: x1 = 42, n1 = 150 and x2 = 76, n2 = 200 6. Claim: p1 7 p2; a = 0.01 Sample statistics: x1 = 6, n1 = 20 and x2 = 4, n2 = 30 Using and Interpreting Concepts Testing the Difference Between Two Proportions In Exercises 7–12, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (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. 7. Multiple Sclerosis Drug In a study to determine the effectiveness of using a drug to treat multiple sclerosis, 488 subjects were given the drug and 244 subjects were given a placebo. The numbers of subjects who had 12-week confirmed disability progression were tracked. The results are shown at the left. At a = 0.01, can you support the claim that there is a difference in the proportion of subjects who had no 12-week confirmed disability progression? (Adapted from The New England Journal of Medicine) 8. Cancer Drug In a study, 760 men with recurrent prostate cancer underwent radiation with or without a type of hormone-based chemotherapy. For 24 months, 384 subjects were given the chemotherapy and 376 subjects were given a placebo. The numbers who survived and did not survive after 12 years were tracked. The results are shown at the left. At a = 0.10, can you support the claim that the proportion of people who survived for 12 years is greater for subjects who were given the chemotherapy than for subjects who were given the placebo? (Adapted from The New England Journal of Medicine) 9. Young Adults In a survey of 3500 males ages 20 to 24 whose highest level of education is some college, but no bachelor’s degree, 80.2% were employed. In a survey of 2000 males ages 20 to 24 whose highest level of education is a bachelor’s degree or higher, 86.4% were employed. At a = 0.01, can you support the claim that there is a difference in the proportion of those employed between the two groups? (Adapted from National Center for Education Statistics) How Many Subjects Had 12-Week Confirmed Disability Progression and How Many Did Not? Drug Placebo 161 327 148 96 Disability progression No disability progression No disability progression FIGURE FOR EXERCISE 7 How Many Subjects Survived for 12 Years and How Many Did Not? Chemotherapy Placebo Did not survive Survived 293 Survived 268 91 108 FIGURE FOR EXERCISE 8
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