HW 3 solutions

# HW 3 solutions - Homework 3 Solutions 8-4 a 95 CI for n 10...

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Homework 3 Solutions 8-4 a) 95% CI for 96 . 1 , 1000 20 , 10 , z x n 4 . 1012 6 . 987 ) 10 / 20 ( 96 . 1 1000 ) 10 / 20 ( 96 . 1 1000 / / n z x n z x b) .95% CI for 96 . 1 , 1000 20 , 25 , z x n 8 . 1007 2 . 992 ) 25 / 20 ( 96 . 1 1000 ) 25 / 20 ( 96 . 1 1000 / / n z x n z x c) 99% CI for 58 . 2 , 1000 20 , 10 , z x n 3 . 1016 7 . 983 ) 10 / 20 ( 58 . 2 1000 ) 10 / 20 ( 58 . 2 1000 / / n z x n z x d) 99% CI for 58 . 2 , 1000 20 , 25 , z x n 3 . 1010 7 . 989 ) 25 / 20 ( 58 . 2 1000 ) 25 / 20 ( 58 . 2 1000 / / n z x n z x e) When n is larger, the CI will get narrower. The higher the confidence level, the wider the CI. 8-7. a) Find n for the length of the 95% CI to be 40. Z a/2 = 1.96 84 . 3 20 2 . 39 20 2 . 39 20 / ) 20 )( 96 . 1 ( length 1/2 2 n n n Therefore, n = 4. b) Find n for the length of the 99% CI to be 40. Z a/2 = 2.58 66 . 6 20 6 . 51 20 6 . 51 20 / ) 20 )( 58 . 2 ( length 1/2 2 n n n Therefore, n = 7.

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8-8 Interval (1): 7 . 3215 9 . 3124 and Interval (2): 1 . 3230 5 . 3110 Interval (1): half-length =90.8/2=45.4 and Interval (2): half-length =119.6/2=59.8 a) 3 . 3170 4 . 45 9 . 3124 1 x 3 . 3170 8 . 59 5 . 3110 2 x The sample means are the same. b) Interval (1): 7 . 3215 9 . 3124 was calculated with 95% Confidence because it has a smaller half-length, and therefore a smaller confidence interval. The 99% confidence level will make the interval larger.
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