Statistics Homework Solutions 130

Statistics Homework Solutions 130 - 130 CHAPTER 5 (b) Let n...

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Unformatted text preview: 130 CHAPTER 5 (b) Let n be the required sample size. ¤ ¡ ¨ ¡ ¨ Replacing p with 0 16484 and solving for n yields n ˜ ¨ 584. The higher the level, the wider the confidence interval. Therefore the narrowest interval, (4.20, 5.83), is the 90% confidence interval, the widest interval, (3.57, 6.46), is the 99% confidence interval, and (4.01, 6.02) is the 95% confidence interval. 11, Y 8 00000, sY ¡ ¡ 0 359039, nX ¨ ¨ 7 909091, sX ¡ ¡ ¨ X 0 154919, nY ¨ ¡ 11. 4. 6. ¡ 9. n ¡ p ˜ ¤ ¥ £ p1 ˜ ¢ 1 96 ¥ Then n satisfies the equation 0 03 The number of degrees of freedom is 2 0 3590392 0 1549192 11 6 0 3590392 11 2 0 1549192 6 11 1 61 ¥ £ ¨ ¤ 14, rounded down to the nearest integer. ¡ ¨ ¨ ¡ £ ¨ ¡ ¤ ¡ ¨ ¨ ¡ 0 420 0 238 . 2 624 0 3590392 11 ¨ 8 00000 ¢ ¥ 2 624, so the confidence interval is 7 909091 0 1549192 , 6 ¨ ¢ ¥ ¨  ¨ ¡ ¡ ¤ Let n be the required sample size. ¡ n 42 ¨ ¤£ 1 645σ ¤£ ¨ ¨ ¡ ¤£ ¨ ¡ ¨ Now n satisfies the equation 0 2 4 2. n. Solving for n yields n ¡ 144, so 1 645σ ¡ 1 645σ 0 35. ¨ Therefore 0 35 The 90% confidence interval based on 144 observations has width ¨ 13. ¡ or 01 2 ¡ ¨ ¢ t14 ¨ ν 441. ¨ 15. (a) False. This a specific confidence interval that has already been computed. The notion of probability does not apply. (b) False. The confidence interval specifies the location of the population mean. It does not specify the location of a sample mean. (c) True. This says that the method used to compute a 95% confidence interval succeeds in covering the true mean 95% of the time. (d) False. The confidence interval specifies the location of the population mean. It does not specify the location of a future measurement. ...
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This note was uploaded on 12/20/2011 for the course STA 3163 taught by Professor Mattgilg during the Fall '11 term at UNF.

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