Review Exercises 457 Section 8.2 In Exercises 11–16, 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. 11. Claim: m1 = m2; a = 0.05. Assume s1 2 = s2 2 Sample statistics: x1 = 228, s1 = 27, n1 = 20 and x2 = 207, s2 = 25, n2 = 13 12. Claim: m1 6 m2; a = 0.10. Assume s1 2 ≠ s2 2 Sample statistics: x1 = 0.015, s1 = 0.011, n1 = 8 and x2 = 0.019, s2 = 0.004, n2 = 6 13. Claim: m1 … m2; a = 0.10. Assume s1 2 ≠ s2 2 Sample statistics: x1 = 664.5, s1 = 2.4, n1 = 40 and x2 = 665.5, s2 = 4.1, n2 = 40 14. Claim: m1 Ú m2; a = 0.01. Assume s1 2 = s2 2 Sample statistics: x1 = 44.5, s1 = 5.85, n1 = 17 and x2 = 49.1, s2 = 5.25, n2 = 18 15. Claim: m1 ≠ m2; a = 0.01. Assume s1 2 = s2 2 Sample statistics: x1 = 61, s1 = 3.3, n1 = 5 and x2 = 55, s2 = 1.2, n2 = 7 16. Claim: m1 7 m2; a = 0.10. Assume s1 2 ≠ s2 2 Sample statistics: x1 = 520, s1 = 25, n1 = 7 and x2 = 500, s2 = 55, n2 = 6 In Exercises 17 and 18, (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. 17. A new method of teaching mathematics is being tested on sixth grade students. A group of sixth grade students is taught using the new curriculum. A control group of sixth grade students is taught using the old curriculum. The mathematics test scores for the two groups are shown in the back-to-back stem-and-leaf plot. Old Curriculum New Curriculum 4 5 8 0 01157 1 16 2 24577 0128 3 47 0269 4 2567 1349 5 157 07 6 235667 3334468 7 002556 19 8 23669 444 9 01468 Key: 60 20 2 = 26 for old curriculum and 22 for new curriculum At a = 0.05, is there enough evidence to support the claim that the new method of teaching mathematics produces higher mathematics test scores than the old method does? Assume the population variances are equal.
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