10.3 EXERCISES SECTION 10.3 Comparing Two Variances 555 For Extra Help: MyLab Statistics Building Basic Skills and Vocabulary 1. Explain how to find the critical value for an F@test. 2. List five properties of the F@distribution. 3. List the three conditions that must be met in order to use a two-sample F@test. 4. Explain how to determine the values of d.f.N and d.f.D when performing a two-sample F@test. Finding a Critical F-Value for a Right-Tailed Test In Exercises 5–8, 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. 5. a = 0.05, d.f.N = 9, d.f.D = 16 6. a = 0.01, d.f.N = 2, d.f.D = 11 7. a = 0.10, d.f.N = 10, d.f.D = 15 8. a = 0.025, d.f.N = 7, d.f.D = 3 Finding a Critical F-Value for a Two-Tailed Test In Exercises 9–12, 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. 9. a = 0.01, d.f.N = 6, d.f.D = 7 10. a = 0.10, d.f.N = 24, d.f.D = 28 11. a = 0.05, d.f.N = 60, d.f.D = 40 12. a = 0.05, d.f.N = 27, d.f.D = 19 In Exercises 13–18, test the claim about the difference between two population variances s 2 1 and s 2 2 at the level of significance a. Assume the samples are random and independent, and the populations are normally distributed. 13. Claim: s 2 1 7 s 2 2; a = 0.10. 14. Claim: s 2 1 = s 2 2; a = 0.05. Sample statistics: s2 1 = 773, Sample statistics: s 2 1 = 310, n1 = 5 and s 2 2 = 765, n2 = 6 n1 = 7 and s 2 2 = 297, n2 = 8 15. Claim: s 2 1 … s 2 2; a = 0.01. 16. Claim: s 2 1 ≠s 2 2; a = 0.05. Sample statistics: s2 1 = 842, Sample statistics: s 2 1 = 245, n1 = 11 and s 2 2 = 836, n2 = 10 n1 = 31 and s 2 2 = 112, n2 = 28 17. Claim: s 2 1 = s 2 2; a = 0.01. 18. Claim: s 2 1 7 s 2 2; a = 0.05. Sample statistics: s2 1 = 9.8, Sample statistics: s 2 1 = 44.6, n1 = 13 and s 2 2 = 2.5, n2 = 20 n1 = 16 and s 2 2 = 39.3, n2 = 12 Using and Interpreting Concepts Performing a Two-Sample F-Test In Exercises 19–26, (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. 19. Life of Appliances Company A claims that the variance of the lives of its appliances is less than the variance of the lives of Company B’s appliances. A sample of the lives of 20 of Company A’s appliances has a variance of 1.8. A sample of the lives of 25 of Company B’s appliances has a variance of 3.9. At a = 0.025, can you support Company A’s claim?
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