mont4e_sm_ch08_sec02 - CHAPTER 8 Section 8-2 8-1 a) The...

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CHAPTER 8 Section 8-2 8-1 a) The confidence level for n x n x / 14 . 2 / 14 . 2 σ μσ + is determined by the value of z 0 which is 2.14. From Table III, Φ (2.14) = P(Z<2.14) = 0.9838 and the confidence level is 2(0.9838-0.5) = 96.76%. b) The confidence level for n x n x / 49 . 2 / 49 . 2 + is determined by the by the value of z 0 which is 2.14. From Table III, Φ (2.49) = P(Z<2.49) = 0.9936 and the confidence level is is 2(0.9936-0.5) = 98.72%. c) The confidence level for n x n x / 85 . 1 / 85 . 1 + is determined by the by the value of z 0 which is 2.14. From Table III, Φ (1.85) = P(Z<1.85) = 0.9678 and the confidence level is 93.56%. 8-2 a) A z α = 2.33 would give result in a 98% two-sided confidence interval. b) A z α = 1.29 would give result in a 80% two-sided confidence interval. c) A z α = 1.15 would give result in a 75% two-sided confidence interval. 8-3 a) A z α = 1.29 would give result in a 90% one-sided confidence interval. b) A z α = 1.65 would give result in a 95% one-sided confidence interval. c) A z α = 2.33 would give result in a 99% one-sided confidence interval. 8-4 a) 95% CI for 96 . 1 , 1000 20 , 10 , = = = = z x n μ 4 . 1012 6 . 987 ) 10 / 20 ( 96 . 1 1000 ) 10 / 20 ( 96 . 1 1000 / / + + σμ 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. 8-1
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8-5. 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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mont4e_sm_ch08_sec02 - CHAPTER 8 Section 8-2 8-1 a) The...

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