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401hw9 - stat 401 Homework 9 solution(Spring 2008 9.2.1 1(a...

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stat 401 Homework 9 solution (Spring, 2008) 9.2.1 1. (a) H 0 : p . 25 vs H a : p > . 25. (b) New design implemented. 2. (a) H a : μ > μ 0 (b) H a : μ < μ 0 (c) For (a), she should but for (b), she should not. 9.3.4 1. (a) Type I (b) Type II 2. Under the null hypothesis X Bin (20 , . 25) (a) P(Type I error)=P( H 0 is rejected when it is true)= P ( X 8 | n = 20 , p = 0 . 25) = 1 - P ( X < 8 | n = 20 , p = 0 . 25) = 1 - P ( X 7 | n = 20 , p = 0 . 25) = 1 - . 968+ . 772 2 = . 13 (b) P(Type II error when p=0.3)=P( H 0 is not rejected when p=0.3)= P ( X < 8 | n = 20 , p = . 3) = P ( X 7 | n = 20 , p = . 3) = . 7772. 9.4.5 3 (a) H 0 : μ = 1 , H a : μ > 1 (b) Z = ¯ X - μ 0 s/ n = 2 . 1 - 1 4 . 1 / 36 = 1 . 61. RR = { z : z > z α } . No assumptions needed since we have sample size greater than 30. (c) Since we have α = 0 . 05, RR = { z : z > z 0 . 05 = 1 . 645 } . Our statistic, z = 1 . 61 is less than critical value 1 . 645. Hence we can not reject null hypothesis. 5 (a) H 0 : p = 0 . 2 , H a : p > 0 . 2 (b) ˆ p = 9 42 Z H 0 = ˆ p - 0 . 2 q 0 . 2(1 - 0 . 2) 42 = 0 . 2314548. Since we have α = 0 . 01, RR = { z : z > z 0 . 01 = 2 . 33 } So we can not reject the null hypothesis. 6 (a) H 0 : e μ = 200 , H a : e μ 6 = 200 (d) Z H 0 = 11 - ( . 5)(16) . 5 16 = 3 2 = 1 . 5. Since | Z H 0 | = 1 . 5 < Z 0 . 05 = 1 . 96, we can not reject the null hypothesis.
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