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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