hw7solu_STAT515Fall2011

# hw7solu_STAT515Fall2011 - Solution to Homework 7(STAT515...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ....
View Full Document

## 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.

### Page1 / 4

hw7solu_STAT515Fall2011 - Solution to Homework 7(STAT515...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online