hw9sol - Solutions to Homework 9 Problem 8.29 a We can...

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Solutions to Homework 9 Problem 8.29 a. We can compute n : n = z 2 α/ 2 σ 2 E 2 = 1 . 96 2 6 . 25 2 2 2 = 37 . 5 . So we should sample at least 38. b. We can compute n : n = z 2 α/ 2 σ 2 E 2 = 1 . 96 2 6 . 25 2 1 2 = 150 . 06 . So we should sample at least 151. Problem 8.35 a. The point estimate of the proportion of office workers who are able to take every telephone call is 281 611 = 0 . 46 . b. The margin of error for a 90% confidence interval is z α/ 2 s ¯ p (1 - ¯ p ) n = 1 . 645 s 0 . 46(1 - 0 . 46) 611 = 0 . 033 . c. The 90% confidence interval is ¯ p ± z α/ 2 s ¯ p (1 - ¯ p ) n = 0 . 46 ± 0 . 033 = (0 . 427 , 0 . 493) . Problem 8.39 a. Here we will use p * = 0 . 156, E = 0 . 03 and z α/ 2 = 1 . 96. The required sample size is n = ( z α/ 2 ) 2 p * (1 - p * ) E 2 = (1 . 96) 2 (0 . 156)(1 - 0 . 156) 0 . 03 2 = 562 . 0 . We would sample at least 562 individuals. b. The only difference from part a is that z α/ 2 = 2 . 575. The required sample size is n = ( z α/ 2 ) 2 p * (1 - p * ) E 2 = (2 . 575) 2 (0 . 156)(1 - 0 . 156) 0 . 03 2 = 970 . 01 . We would sample at least 971 individuals. 1
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Problem 8.43(b,c) b. We have ¯ p = 0 . 31 and n = 1500. The margin of error for a 95% confidence interval is
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