8.2 EXERCISES 432 CHAPTER 8 Hypothesis Testing with Two Samples For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. What conditions are necessary to use the t@test for testing the difference between two population means? 2. Explain how to perform a two-sample t@test for the difference between two population means. In Exercises 3–8, use Table 5 in Appendix B to find the critical value(s) for the alternative hypothesis, level of significance a, and sample sizes n1 and n2. Assume that the samples are random and independent, the populations are normally distributed, and the population variances are (a) equal and (b) not equal. 3. Ha: m1 ≠ m2, a = 0.10, n1 = 11, n2 = 14 4. Ha: m1 7 m2, a = 0.01, n1 = 12, n2 = 15 5. Ha: m1 6 m2, a = 0.05, n1 = 7, n2 = 11 6. Ha: m1 ≠ m2, a = 0.01, n1 = 19, n2 = 22 7. Ha: m1 7 m2, a = 0.05, n1 = 13, n2 = 8 8. Ha: m1 6 m2, a = 0.10, n1 = 30, n2 = 32 In Exercises 9–12, test the claim about the difference between two population means m1 and m2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. 9. Claim: m1 = m2; a = 0.01. Assume s1 2 = s2 2 Sample statistics: x1 = 33.7, s1 = 3.5, n1 = 12 and x2 = 35.5, s2 = 2.2, n2 = 17 10. Claim: m1 6 m2; a = 0.10. Assume s1 2 = s2 2 Sample statistics: x1 = 0.345, s1 = 0.305, n1 = 11 and x2 = 0.515, s2 = 0.215, n2 = 9 11. Claim: m1 … m2; a = 0.05. Assume s1 2 ≠ s2 2 Sample statistics: x1 = 2410, s1 = 175, n1 = 13 and x2 = 2305, s2 = 52, n2 = 10 12. Claim: m1 7 m2; a = 0.01. Assume s1 2 ≠ s2 2 Sample statistics: x1 = 52, s1 = 4.8, n1 = 32 and x2 = 50, s2 = 1.2, n2 = 40 Using and Interpreting Concepts Testing the Difference Between Two Means In Exercises 13–22, (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 t, (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. 13. Pet Food A pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples of the two types of pets are shown at the left. At a = 0.10, can you reject the pet association’s claim? Assume the population variances are equal. (Adapted from American Pet Products Association) Sample Statistics for Annual Costs of Pet Food Dogs Cats x1 = $255 s1 = $30 n1 = 16 x2 = $231 s2 = $28 n2 = 18 TABLE FOR EXERCISE 13
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