7 Review Exercises 406 CHAPTER 7 Hypothesis Testing with One Sample Section 7.1 In Exercises 1–6, the statement represents a claim. Write its complement and state which is H0 and which is Ha. 1. m … 375 2. m = 82 3. p 6 0.205 4. m ≠ 150,020 5. s 7 1.9 6. p Ú 0.64 In Exercises 7–10, (a) state the null and alternative hypotheses and identify which represents the claim, (b) describe type I and type II errors for a hypothesis test of the claim, (c) explain whether the hypothesis test is left-tailed, right-tailed, or two-tailed, (d) explain how you should interpret a decision that rejects the null hypothesis, and (e) explain how you should interpret a decision that fails to reject the null hypothesis. 7. A polling organization reports that the proportion of U.S. adults who believe that Earth’s temperature has been increasing over the past 100 years is 81%. (Source: Resources) 8. An agricultural cooperative guarantees that the mean shelf life of a type of dried fruit is at least 400 days. 9. A nonprofit consumer organization says that the standard deviation of the starting prices of its top-rated vehicles for a recent year is no more than $2900. (Adapted from U.S. News) 10. An energy bar maker claims that the mean number of grams of carbohydrates in one bar is less than 25. Section 7.2 In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance a. 11. Left-tailed test, z = -0.94, a = 0.05 12. Two-tailed test, z = 2.57, a = 0.10 In Exercises 13–16, find the critical value(s) and rejection region(s) for the type of z-test with level of significance a. Include a graph with your answer. 13. Left-tailed test, a = 0.02 14. Two-tailed test, a = 0.005 15. Right-tailed test, a = 0.025 16. Two-tailed test, a = 0.03 In Exercises 17–20, state whether the standardized test statistic z allows you to reject the null hypothesis. Explain your reasoning. 17. z = 1.631 18. z = 1.723 19. z = -1.464 20. z = -1.655 In Exercises 21–24, test the claim about the population mean m at the level of significance a. Assume the population is normally distributed. 21. Claim: m … 45; a = 0.05; s = 6.7. Sample statistics: x = 47.2, n = 22 22. Claim: m ≠ 8.45; a = 0.03; s = 1.75. Sample statistics: x = 7.88, n = 60 23. Claim: m 6 5.500; a = 0.01; s = 0.011. Sample statistics: x = 5.497, n = 36 24. Claim: m = 7450; a = 0.10; s = 243. Sample statistics: x = 7495, n = 27 z −z0 = −1.645 z0 = 1.645 1 2 3 −1 −2 −3 0 FIGURE FOR EXERCISES 17–20
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