8.3 EXERCISES 442 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 dependent samples t@test for the mean of the differences for a population of paired data? 2. Explain what the symbols d and sd represent. In Exercises 3–8, test the claim about the mean of the differences for a population of paired data at the level of significance a. Assume the samples are random and dependent, and the populations are normally distributed. 3. Claim: md 6 0; a = 0.05. Sample statistics: d = 1.5, sd = 3.2, n = 14 4. Claim: md = 0; a = 0.01. Sample statistics: d = 3.2, sd = 8.45, n = 8 5. Claim: md … 0; a = 0.10. Sample statistics: d = 6.5, sd = 9.54, n = 16 6. Claim: md 7 0; a = 0.05. Sample statistics: d = 0.55, sd = 0.99, n = 28 7. Claim: md Ú 0; a = 0.01. Sample statistics: d = -2.3, sd = 1.2, n = 15 8. Claim: md ≠0; a = 0.10. Sample statistics: d = -1, sd = 2.75, n = 20 Using and Interpreting Concepts Testing the Difference Between Two Means In Exercises 9–20, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) calculate d and sd, (d) find the standardized test statistic t, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed. 9. Migraines A researcher claims that injections of onabotulinumtoxinA reduce the number of days per month that chronic migraine sufferers have headaches. The table shows the number of days chronic migraine sufferers suffered migraines before and after using the treatment. At a = 0.01, is there enough evidence to support the researcher’s claim? (Adapted from Journal of Headache and Pain) Patient 1 2 3 4 5 6 7 8 9 Days (before) 20 17 15 27 22 18 25 20 27 Days (after) 01511145 6 1 4 5 Patient 10 11 12 13 14 15 16 17 18 Days (before) 24 22 19 15 31 25 19 15 16 Days (after) 13212310714015
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