Statistics Homework Solutions 115

Statistics Homework Solutions 115 - 115 SECTION 5.1 Chapter...

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Unformatted text preview: 115 SECTION 5.1 Chapter 5 Section 5.1 1. (a) 1.96 (b) 2.33 (c) 2.57 or 2.58 (d) 1.28 The level is the proportion of samples for which the confidence interval will cover the true value. Therefore as the level goes up, the reliability goes up. This increase in reliability is obtained by increasing the width of the confidence interval. Therefore as the level goes up the precision goes down. 100, z 025 ¨ ¡ ¨ ¨ ¨ ¡ ¡ 521. ¨ ¡ §¥ ¡¥ ¡¥ 1 96. ¨ 100 , or 145 10 154 90 . ¥ ¨  ¨ ¤ ¥ ¤£ ¤ ¨ 100 , or 143 55 156 45 .  ¨ ¤ ¥ ¤£ 2 58 25 ¨ ¡ ¤ ¨ ¤ ¡ ¤£ ¤£ ¡ ¡ ¡ ¡ ¡ ¤ ¨ ¤ ¡ ¨ 2 58. ¥ ¡ ¦ ¡ ¨ ¨ ¨ ¡ ¡ ¡ ¡ ¡ The confidence interval is 150 301. 1 96 25 100, z 005 ¨ ¡ 25, n £ ¦ ¡ 150, s ¡ ¡ 25, so n The confidence interval is 150 (b) X 0 7416, or 74.16%. 25, so n 100, z 025 0 1292. ¨ ¨ n ¡ n 0 1292, so α 2 ¡ 2 0 1292 0 8708 ¢ 1 13 is 1 2 ¤¦ 1 13. zα 221 ¤£ 2 6230 100 . ¥ 2 58. 2 58 221 25, n ¨ 1 96. 1 96 221 150, s ¤ 7. (a) X ¤£ ¡ (e) z 005 ¥ ¡ (d) z 025 1 ¤ yields zα α ¨ 100, so the upper confidence bound 6255 satisfies 6255 The area to the right of z The level is 1 100 , or 6173 0 6287 0 . ¥¨ ¡ 2 2 58 221 Solving for zα ¡ 221, n 2 58. ¨ 6230, s ¤ (c) X ¤£ ¡ The confidence interval is 6230 ¥ 100, z 005 100 , or 6186 7 6273 3 . ¤ ¡ 221, n 6230, s 1 96 221 ¨ ¡ The confidence interval is 6230 (b) X 1 96. ¥¨ 221, n 6230, s ¡ 5. (a) X ¨ 3. ...
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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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