chapter_21 - CHAPTER 21 SOLUTIONS AND MINI-PROJECT NOTES...

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CHAPTER 21 SOLUTIONS AND MINI-PROJECT NOTES CHAPTER 21 THE ROLE OF CONFIDENCE INTERVALS IN RESEARCH EXERCISE SOLUTIONS 21.1 No. You also need the sample standard deviation. 21.2 Using Example 1, the sample mean weight loss for the 42 men who dieted was 7.2 kg. The corresponding population mean is the hypothetical average weight loss that would be achieved if all men similar to this group were to follow a diet similar to the one used by this group, for the same amount of time. 21.3 a. The standard error of the mean is 0.5/ 36 = 0.5/6 = 1/12 or 0.083 hours or 5 minutes. b. A 95% confidence interval is 12 hrs 50 min to 13 hrs 10 min. c. The SEM for the Dutch babies is 0.062, so the "measure of variability" is the square root of (0.083) 2 + (0.062) 2 = 0.104. A 95% confidence interval for the difference is 2 ± 2(0.104) or 1.79 to 2.21 hours. 21.4 5%. 21.5 No. They would have the necessary information on the entire population so they could compute it directly. 21.6 a. We could be 95% confident that the two population means are not equal. b. The population means could be (but are not necessarily) the same. 21.7 a. With 95% confidence we could conclude that the risk of disease was greater under one of the conditions than the other. b. We could not conclude that the risks under the two conditions were different (but we would not go so far as to say they are equal.) 21.8 a. A 90% confidence interval is 29 ± (1.645)(16.3) or 2.2 to 55.8. b. Yes, because this interval does not cover zero. (The 95% confidence interval did cover 0.) 21.9 a. A 95% confidence interval extends from 64 to 112. b. A 95% confidence interval extends from 95 to 139. c. No. Because there is overlap in the intervals we cannot be confident that the true means are indeed different. 21.10 This would have been misleading because the interval does not lie entirely above zero, so there is a good chance that the difference in the sample means does not represent a real difference in the population means at all, or that there is a difference in the opposite direction. 21.11 a. The confidence interval is 64.64 ± 0.81 or 63.83 to 65.45. b. The confidence interval is 63.97 ± 2.0 or 61.97 to 65.97. c. The interval in part b is wider because the sample size is smaller. We could not conclude that there is a difference in the mean ages because there is overlap in the two intervals. d.
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This note was uploaded on 10/15/2011 for the course STAT 100 at Penn State.

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chapter_21 - CHAPTER 21 SOLUTIONS AND MINI-PROJECT NOTES...

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