hw7solu_STAT515Fall2011

hw7solu_STAT515Fall2011 - Solution to Homework 7(STAT515...

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Unformatted text preview: Solution to Homework 7 (STAT515, Fall 2011) 7.10. ( 15 points ) Given n = 90 (large sample), ¯ x = 25 . 9, and s = 2 . 7 , a. A 95% confidence interval for μ is given by ¯ x ± z . 025 s √ n = 25 . 9 ± 1 . 96 × 2 . 7 √ 90 ⇒ (25 . 34 , 26 . 46) . b. A 90% confidence interval for μ is given by ¯ x ± z . 05 s √ n = 25 . 9 ± 1 . 645 × 2 . 7 √ 90 ⇒ (25 . 43 , 26 . 37) . c. A 99% confidence interval for μ is given by ¯ x ± z . 005 s √ n = 25 . 9 ± 2 . 575 × 2 . 7 √ 90 ⇒ (25 . 17 , 26 . 63) . 7.12. ( 15 points ) We have ¯ x = 33 . 9 and s = 3 . 3 , a. With n = 100, a 95% confidence interval for μ is given by ¯ x ± z . 025 s √ n = 33 . 9 ± 1 . 96 × 3 . 3 √ 100 ⇒ (33 . 2532 , 34 . 5468) . b. With n = 400, a 95% confidence interval for μ is given by ¯ x ± z . 025 s √ n = 33 . 9 ± 1 . 96 × 3 . 3 √ 400 ⇒ (33 . 5766 , 34 . 2234) . c. The width of the confidence interval in part a is 34 . 5468- 33 . 2532 = 1 . 2936 . The width of the confidence interval in part b is 34 . 2234- 33 . 5766 = 0 . 6468 . Hence, holding the confidence coefficient fixed, by quadrupling the sample size, the width of a confidence interval reduces to half of the original width. 7.14. ( 12 points ) Given n = 2819 (large sample), ¯ x = 14 . 6, and s = 9 . 8 , a. A point estimate for the mean personal network size of all older adults, μ, is ¯ x = 14 . 6 ....
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This note was uploaded on 02/21/2012 for the course STAT 515 taught by Professor Zhao during the Fall '10 term at South Carolina.

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hw7solu_STAT515Fall2011 - Solution to Homework 7(STAT515...

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