7.3 homework

BUILDING BASIC SKILLS AND VOCABULARY 1. Explain how to find critical values for a t @ distribution. 2. Explain how to use a t @ test to test a hypothesized mean m when s is unknown. What assumptions are necessary? In Exercises 3– 8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance a and sample size n. 3. Left-tailed test, a = 0.10, n = 20 4. Left-tailed test, a = 0.01, n = 35 5. Right-tailed test, a = 0.05, n = 23 6. Right-tailed test, a = 0.01, n = 31 7. Two-tailed test, a = 0.05, n = 27 8. Two-tailed test, a = 0.10, n = 38 Graphical Analysis In Exercises 9 and 10, state whether each standardized test statistic t allows you to reject the null hypothesis. Explain. 9. (a) t = 2.091 10. (a) t = 1.705 (b) t = 0 (b) t = - 1.755 (c) t = - 1.08 (c) t = - 1.585 (d) t = - 2.096 (d) t = 1.745 t t 0 = − 2.086 2 3 4 1 − 1 − 3 − 4 0 t − t 0 = − 1.725 t 0 = 1.725 2 3 4 1 − 1 − 3 − 2 − 4 0 In Exercises 11–14, test the claim about the population mean m at the level of significance a . Assume the population is normally distributed. If convenient, use technology. 11. Claim: m = 15; a = 0.01. Sample statistics: x = 13.9, s = 3.23, n = 36 12. Claim: m 7 25; a = 0.05. Sample statistics: x = 26.2, s = 2.32, n = 17 13. Claim: m Ú 8000; a = 0.01. Sample statistics: x = 7700, s = 450, n = 25 14. Claim: m ≠ 52,200; a = 0.05. Sample statistics: x = 53,220, s = 2700, n = 34 USING AND INTERPRETING CONCEPTS Testing Claims Using Rejection Regions In Exercises 15–22, (a) identify the claim and state H 0 and H a , (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 population is normally distributed. If convenient, use technology. 15. Used Car Cost A used car dealer says that the mean price of a three-year-old sports utility vehicle (in good condition) is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,640 and a standard deviation of $1990. Is there enough evidence to reject the claim at a = 0.05? 7.3 Exercises