Chapter_4_Recommended_Homework_Solutions

Chapter_4_Recommended_Homework_Solutions - Chapter 4...

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Chapter 4 Recommended Homework Solutions 4-11. a) α = P(reject H 0 when H 0 is true) = P( X 13.7 when μ = 14) = - σ μ - 5 / 3 . 0 14 7 . 13 n / X P = P(Z - 2.23) = 0.0129. The probability of rejecting the null hypothesis when it is true is 0.0129. b) β = P(accept H 0 when μ = 13.5) = ( 29 5 . 13 when 7 . 13 X P = μ = - σ μ - 5 / 3 . 0 5 . 13 7 . 13 n / X P P(Z > 1.49) = 1 - P(Z 1.49) = 1 - 0.931888= 0.0681 The probability of accepting the null hypothesis when it is false is 0.0681. c) 1 - β = 1 – 0.0681 = 0.9319 4-12. a) α = P( X 13.7 when μ = 14) = - - 16 / 3 . 0 14 7 . 13 n / X P σ μ = P(Z - 4) = 0. The probability of rejecting the null, when the null is true, is 0 with a sample size of 16. b) β = P( X > 13.7 when μ =13.5) = 13.7 13.5 / 0.3/ 16 X P n μ σ - - = P(Z > 2.67) = 1 - P(Z 2.67) = 1 – 0.99621 = 0.00379. The probability of accepting the null hypothesis when it is false is 0.00379. c) 1 - β = 1 – 0.00379 = 0.99621 4-13. Find the boundary of the critical region if α = 0.01: a) 0.01 = - 5 / 3 . 0 14 c Z P What Z value will give a probability of 0.01? Using Table 1 in the appendix, Z value is - 2.33. Thus, 5 / 3 . 0 14 c - = - 2.33, c = 13.687 b) β = P( X > 13.687 when μ =13.5) = 13.687 13.5 / 0.3/ 5 X P n - - = P(Z > 1.39) = 1 - P(Z 1.39) = 1 – 0.917736 = 0.092264. The probability of accepting the null hypothesis when it is false is 0.092264. c) 1 - β = 1 – 0.092264 = 0.907736 4-14. 0.05 = - 16 / 3 . 0 14 c Z P What Z value will give a probability of 0.05? Using Table 1 in the appendix, Z value is - 1.65. Thus, 16 / 3 . 0 14 c - = - 1.65, c = 13.876 b) β = P( X > 13.876 when μ =13.5) = - σ μ - 16 / 3 . 0 5 . 13 876 . 13 / n X P = P(Z > 5.01) = 1 - P(Z 5.01) = 1 – 1 = 0. The probability of accepting the null hypothesis when it is false is 0. c) 1 - β = 1 – 0 = 1
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4-21. a) α = P( X 8.85 when μ = 9) + P( X 9.15 when μ = 9) = - - 10 / 25 . 0 9 85 . 8 8 / 25 . 0 9 X P + - - 10 / 25 . 0 9 15 . 9 10 / 25 . 0 9 X P = P(Z - 1.9) + P(Z 1.9) = P(Z -1.9) + (1 - P(Z 1.9)) = 0.028717 + 0.028717 = 0.0574. b) Power = 1 - β β = P(8.85 X 9.15 when μ = 9.1) = - - - 10 / 25 . 0 1 . 9 15 . 9 10 / 25 . 0 1 . 5 X 10 / 25 . 0 1 . 9 85 . 8 P = P( - 3.16 Z 0.63) = P(Z 0.63) - P(Z - 3.16) = 0.735653 - 0.000789 = 0.7349 1 - β = 0.265. 4-22. Using n = 16: a) α = P( X 8.85 when μ = 9) + P( X > 9.15 when μ = 9) = - - 16 / 25 . 0 9
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This note was uploaded on 06/26/2008 for the course IEE 380 taught by Professor Anderson-rowland during the Fall '06 term at ASU.

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Chapter_4_Recommended_Homework_Solutions - Chapter 4...

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