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ps5_answer - Econ 41 Statistics for Economists Summer 2007...

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1 Econ 41 Statistics for Economists Summer 2007 Chunming Yuan Problem Set 5 (Answers) Multiple Choice Summary Table Item Answer Item Answer 1. c 18. d 2. d 19. c 3. b 20 d 4. b 21 d 5. c 22 c 6. b 23 a 7. b 24 d 8. a 25 c 9. c 26 b 10. c 27 b 11. c 28 c 12. c 29 a 13. b 30 d 14. c 31 d 15. c 32 c 16. b 33 a 17. b 34 b Problem and Essay Solutions 1. 50 4 8 / . = x s = 1.188 At 95% confidence, z = 1.96. Therefore, the confidence interval is 75.8 ± (1.96)(1.188) = 75.8 ± 2.26 = 73.54 to 78.06 lbs. At 95% confidence, z = 2.33. Therefore, the confidence interval is 75.8 ± (2.33)(1.188) = 75.8 ± 2.77 = 73.03 to 78.57 lbs. At 99% confidence, z = 2.58. Therefore, the confidence interval is 75.8 ± (2.58)(1.188) = 75.8 ± 3.07 = 72.73 to 78.87 lbs. 2. 28 10 / = x s = 1.89 At 90% confidence and 27 df , t = 1.703. Therefore, the confidence interval is 45 ± 1.703(1.89) = 45 ± 3.22 = 41.78 to 48.22 minutes. 3. a. 25 001 / . = x s = .0002 The sample size is less than 30, so we should use the t distribution.

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2 At 95% confidence and 24 df , t = 2.064. Therefore, the confidence interval is .003 ± 2.064(.0002) = .003 ± .0004 = .0026 to .0034 in. b. 30 01 / . = x s = .00183 The sample size is 30, so we can use the normal distribution. At 95% confidence, z = 1.96. Therefore, the confidence interval is .011 ± 1.96(.00183) = .011 ± .0036 = .0074 to .0146 in. 4. Critical value: z = –2.33 Test statistic: 69 110 410 500 475 2 250 11 840 10 . / , , , = = z = –3.70 The value of the test statistic lies in the rejection region. Therefore, reject the null hypothesis. 5.
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ps5_answer - Econ 41 Statistics for Economists Summer 2007...

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