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# ch08 - CHAPTER 8 Section 8-2 8-1 a The confidence level for...

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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 µ + is determined by the value of z 0 which is 2.14. From Table II, 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 II, 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 II, 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 4 . 1012 6 . 987 ) 10 / 20 ( 96 . 1 1000 ) 10 / 20 ( 96 . 1 1000 / / + + 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 8-1

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8-5 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. 8-6 Interval (1): 7 . 3215 9 . 3124 µ and Interval (2): 1 . 3230 5 . 3110 Interval (1): half-length =90.8/2=45.4 and Interval (2): half-length =119.6/2=59.8 a) 3 . 3170 4 . 45 9 . 3124 1 = + = x 3 . 3170 8 . 59 5 . 3110 2 = + = x The sample means are the same. b) Interval (1): 7 . 3215 9 . 3124 was calculated with 95% Confidence because it has a smaller half-length, and therefore a smaller confidence interval. The 99% confidence level will make the interval larger. 8-7 a) The 99% CI on the mean calcium concentration would be longer. b) No, that is not the correct interpretation of a confidence interval. The probability that is between 0.49 and 0.82 is either 0 or 1. c) Yes, this is the correct interpretation of a confidence interval. The upper and lower limits of the confidence limits are random variables. 8-8 95% Two-sided CI on the breaking strength of yarn: where x = 98, σ = 2 , n=9 and z 0.025 = 1.96 3 . 99 7 . 96 9 / ) 2 ( 96 . 1 98 9 / ) 2 ( 96 . 1 98 / / 025 . 0 025 . 0 + + σ n z x n z x 8-9 95% Two-sided CI on the true mean yield: where x = 90.480, σ = 3 , n=5 and z 0.025 = 1.96 11 . 93 85 . 87 5 / ) 3 ( 96 . 1 480 . 90 5 / ) 3 ( 96 . 1 480 . 90 / / 025 . 0 025 . 0 + + n z x n z x 8-10 99% Two-sided CI on the diameter cable harness holes: where x =1.5045 , σ = 0.01 , n=10 and z 0.005 = 2.58 5127 . 1 4963 . 1 10 / ) 01 . 0 ( 58 . 2 5045 . 1 10 / ) 01 . 0 ( 58 . 2 5045 . 1 / / 005 . 0 005 . 0 + + n z x n z x 8-2
8-11 a) 99% Two-sided CI on the true mean piston ring diameter For α = 0.01, z α /2 = z 0.005 = 2.58 , and x = 74.036, σ = 0.001, n=15 xz n n ≤≤+ 0 005 0 005 ..

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ch08 - CHAPTER 8 Section 8-2 8-1 a The confidence level for...

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