Chap009

Chap009 - CHAPTER 9 ESTIMATION AND CONFIDENCE INTERVALS 1 2...

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C HAPTER 9 E STIMATION AND CONFIDENCE I NTERVALS 1. 51.314 and 58.686, found by 55 2.58(10/ 49) . 2. 38.911 and 41.089, found by 40 1.96(5/ 81) . 3. a. 1.581, found by 5/ 10 X σ = b. The population is normally distributed and the population variance is known. c. 16.901 and 23.099, found by 20 ± 3.099 4. 1.44 5. a. \$20. It is our best estimate of the population mean. b. \$18.60 and \$21.40, found by \$20 1.96(\$5/ 49) . about 95 percent of the intervals similarly constructed will include the population mean. 6. a. \$18.775 and \$21.225, found by \$20 1.96(\$5/ 64) . b. The confidence interval is based on the standard error computed by / s n . As n , the sample size, increases (in this case from 49 to 64) the standard error decreases and the confidence interval becomes smaller. 7. a. 8.60 gallons b. 7.83 and 9.37, found by 8.60 2.58(2.30/ 60) . c. If 100 such intervals were determined, the population mean would be included in about 99 intervals. 8. 5.29 and 6.81 errors found by 6.05 1.96(2.44/ 40) . 9. a. 2.201 b. 1.729 c. 3.499 10. a. 2.145 b. 2.500 c. 1.796 11. a. The population mean is unknown, but the best estimate is 20, the sample mean. b. Use the t distribution as the standard deviation is unknown and the sample size is small. However, assume the population is normally distributed. c. 2.093 d. Between 19.06 and 20.94, found by 2 20 2.093 20 . e. Neither value is reasonable because they are not inside the interval. Chapter 9 81

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12. a. The population mean is unknown, but the best estimate is 60, the sample mean. b. Use the t distribution as the standard deviation is unknown and the sample size is small. However, assume the population is normally distributed. c. 1.753 d. Between 51.235 and 68.765, found by 20 60 1.753 16 . e. That value is reasonable because it is inside the interval. 13. Between 95.39 and 101.81, found by 5.54 98.6 1.833 10 . 14. Between 30.99 and 39.15, found by 6.02 35.07 2.624 15 . 15.
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Chap009 - CHAPTER 9 ESTIMATION AND CONFIDENCE INTERVALS 1 2...

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