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hw9sol - STAT401 Homework 9 Solutions(Spring 2009 8.4.3 1 n...

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STAT401: Homework 9 Solutions (Spring 2009) 8.4.3 1. n = ( 2 · Z . 01 · σ L ) 2 = ( 2 × 2 . 38 × 1 . 2 . 4 ) 2 = 195 . 44. We need n = 196. 3. n = ( 2 · Z . 1 · σ L ) 2 = ( 2 × 1 . 285 × 18 5 ) 2 = 85 . 6. We need n = 86. 5. ˆ p = 9 40 , L = . 1. n = 4 · Z 2 α/ 2 ˆ p (1 - ˆ p ) L 2 = 4 · 1 . 645 2 · (9 / 40)(1 - 9 / 40) . 1 2 = 188 . 7452. We need n = 189. If we don’t have information, we use ˆ p = . 5 instead. Therefore we need n = 271, because 1 . 645 2 . 1 2 = 270 . 55 8.5.3 2. t 0 . 05 , 7 = 1 . 895 , 90% P.I is (¯ x ± t 0 . 05 , 7 ± · S · q 1 + 1 n ) = (30 . 79 ± 1 . 895 · 6 . 93 · q 1 + 1 8 ) = (17 . 665 , 43 . 915) (b) The data are normally distributed. 4. (a) Yes. (b) No. (c) ˆ μ Y | X =372 . 8 = 193 . 9643 + 0 . 9338404 × 372 . 8 = 542 . 1 t * . 05 , 8 = 1 . 860, S = 4118 . 563 = 64 . 17603 90% P.I is 542 . 1 ± 1 . 860 · 64 . 17603 · q 1 + 1 10 = 542 . 1 ± 125 . 1936 = (416 . 9064 , 667 . 2936) 9.2.1 1. (a) H 0 : p 0 . 25 vs H a : p > 0 . 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. 9.3.6 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
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