Statistics Homework Solutions 118

Statistics Homework Solutions 118 - 118 CHAPTER 5 23. (a)...

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Unformatted text preview: 118 CHAPTER 5 23. (a) False. The confidence interval is for the population mean, not the sample mean. The sample mean is known, so there is no need to construct a confidence interval for it. n , which is a 95% confidence interval for the population ¤£ 1 96 s ¥ ¤ ¨ (b) True. This results from the expression X mean. (c) False. The standard deviation of the mean involves the square root of the sample size, not of the population size. 25. The supervisor is underestimating the confidence. The statement that the mean cost is less than $160 is a one-sided upper confidence bound with confidence level 97.5%. Section 5.2 ¡ 1 96. ¤ ¥ £ 50 ¤ ¥ £ 70 4 , or (0.603, 0.842). 4 , or (0.565, 0.879). ¢ 50 ¢ 0 72222 ¤ ¥ £ ¨ 1 96 0 72222 1 ¢ ¤ ¡ ¨ ¤ ©¥ £ ¢ ¤ ¡ ¡ ¡ The confidence interval is 0 72222 0 72222, z 025 4 , or (0.629, 0.831). ¥ 4 ¢ 50 ¡¥ 2 ¨ 37 50, p ˜ ¡ ¡ 37, n 0 74 ¨ £ (b) X ¡ 37 50 ¨ 1. (a) p ¨ ¨ (c) Let n be the required sample size. ¤ ¡ ¨ ¨ ¢ 2 58. 2 58 0 72222 1 0 72222 ¨ ¤ ¨ ¤ ©¥ £ ¢ ¤ ¡ ¡ ¡ The confidence interval is 0 72222 0 72222, z 005 ¡¥ 4 ¨ 50 2 ¡ 37 ¡ ¨ 50, p ˜ ¨ ¡ 37, n 4. 74. ¡ (d) X n ¥ p ˜ ¤ ¥ £ p1 ˜ ¢ 1 96 ¥ Then n satisfies the equation 0 10 Replacing p with 0 72222 and solving for n yields n ˜ ¨ ¨ (e) Let n be the required sample size. 1 96. 0 72973 1 645. ¤ ¥ £ 0 72973 70 ¢ ¨ ¡ ¡ ¡¥ ¨ 1 645 0 72973 1 ¨ ¨ ¤ ¨ ¨ ¢ ¤ ¡ ¡ ¡ ¨ ¢ ¤ ©¥ £ ¢ ¤ ¡ ¡ ¡ The confidence interval is 0 72973 4 ¨ 70 ¤ ¤ ¥ £ 2 ¢ 52 0 72973, z 05 1 96 0 72973 1 70, p ˜ ¡¥ 52, n ¨ The confidence interval is 0 72973 (b) X 0 72973, z 025 ¨ 4 ¡ 70 ¨ ¨ 2 ¡ ¡ 52 ¡ ¨ 70, p ˜ 130. 4 , or (0.645, 0.815). ¥ ¤ 52, n 4. ¥ ¡ Replacing p with 0 72222 and solving for n yields n ˜ 3. (a) X n ¨ p ˜ ¤ ¥ £ p1 ˜ ¢ 2 58 ¥ Then n satisfies the equation 0 10 ¨ ...
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