HW 4 solutions

# HW 4 solutions - Homework 4 Solutions 2 8-43 99 lower...

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Homework 4 Solutions 8-43 99% lower confidence bound for 2 For = 0.01 and n = 15, 2 1 , n 2 14 , 01 . 0 29.14 2 2 2 00003075 . 0 14 . 29 ) 008 . 0 ( 14 8-52 a) 99% two-sided confidence interval on 2 913 . 1 10 s n 59 . 23 2 9 , 005 . 0 and 73 . 1 2 9 , 995 . 0 038 . 19 396 . 1 73 . 1 ) 913 . 1 ( 9 59 . 23 ) 913 . 1 ( 9 2 2 2 2 b) 99% lower confidence bound for 2 For = 0.01 and n = 10, 2 1 , n 2 9 , 01 . 0 21.67 2 2 2 5199 . 1 67 . 21 ) 913 . 1 ( 9 c) 90% lower confidence bound for 2 For = 0.1 and n = 10, 2 1 , n 2 9 , 1 . 0 14.68 498 . 1 2436 . 2 68 . 14 ) 913 . 1 ( 9 2 2 2 d) The lower confidence bound of the 99% two-sided interval is less than the one-sided interval. The lower confidence bound for 2 is in part (c) is greater because the confidence is lower. 8-58 a) 95% Confidence Interval on the true proportion of helmets showing damage 36 . 0 50 18 ˆ p 50 n 96 . 1 2 / z

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493 . 0 227 . 0 50 ) 64 . 0 ( 36 . 0 96 . 1 36 . 0 50 ) 64 . 0 ( 36 . 0 96 . 1 36 . 0 ) ˆ 1 ( ˆ ˆ ) ˆ 1 ( ˆ ˆ 2 / 2 / p p n p p z p p n p p z p b) 76 . 2212 ) 36 . 0 1 ( 36 . 0 02 . 0 96 . 1 ) 1 ( 2 2 2 / p p E z n 2213 n c) 2401 ) 5 . 0 1 ( 5 . 0 02 . 0 96 . 1 ) 1 ( 2 2 2 / p p E z n 8-40 95% lower bound confidence for the mean wall thickness given x = 4.05 s = 0.08 n = 25 t ,n-1 = t 0.05,24 = 1.711 n s t x 24 , 05 . 0
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