# ch08 - CHAPTER 8 Section 8-2 8-7 a The 99 CI on the mean...

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Unformatted text preview: CHAPTER 8 Section 8-2 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 μ 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. 8.13 a) 95% two sided CI on the mean compressive strength z α /2 = z 0.025 = 1.96, and f8e5 x = 3250, σ 2 = 1000, n=12 x z n x z n- ≤ ≤ + 0 025 0 025 . . σ μ σ 89 . 3267 3232.11 12 62 . 31 96 . 1 3250 12 62 . 31 96 . 1 3250 e e e e e e e e +- μ μ b) 99% Two-sided CI on the true mean compressive strength z α /2 = z 0.005 = 2.58 e e e e e e +- n z x n z x s m s 005 . 005 . 6 . 3273 3226.4 12 62 . 31 58 . 2 3250 12 62 . 31 58 . 2 3250 e e e e e e e e +- μ μ The 99% CI is wider than the 95% CI 8.17 To decrease the length of the CI by one half, the sample size must be increased by 4 times (2 2 ). l n z 5 . / 2 / = σ α Now, to decrease by half, divide both sides by 2. 4 / ) 2 / ( 4 / ) 2 / ( 2 / ) 2 / ( 2 / ) / ( 2 2 / 2 / 2 / l n z l n z l n z = = = σ σ σ α α α Therefore, the sample size must be increased by 2 2 . Section 8-3 8-27 99% upper confidence interval on mean SBP 9 . 9 3 . 118 14 = = = σ ξ ν 650 . 2 13 , 01 . = τ 8-1 312 . 125 14 9 . 9 650 . 2 3 . 118 13 , 005 . e e e e e e e + + μ μ μ ν σ τ ξ 8.3199% confidence interval on mean current required Assume that the data are a random sample from a normal distribution. 7 . 15 2 . 317 10 = = = σ ξ ν 250 . 3 9 , 005 . = τ 34 . 333 06 . 301 10 7 . 15 250 . 3 2 . 317 10 7 . 15 250 . 3 2 . 317 9 , 005 . 9 , 005 . e e e e e e e e e e +- +- μ μ μ ν σ τ ξ ν σ τ ξ 8-37 a) The data appear to be normally distributed. There is not strong evidence that the percentage of enrichment deviates from normality. b) 99% two-sided confidence interval on mean percentage enrichment For α = 0.01 and n = 12, t α /2,n-1 = t 0.005,11 = 3.106, 0.0993 s 2.9017 = = ξ 991 . 2 813 . 2 12 0.0993 106 . 3 902 . 2 12 0.0993 106 . 3 902 . 2 11 , 005 . 11 , 005 ....
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## This note was uploaded on 09/03/2009 for the course STATISTICS EGN 3443 taught by Professor Aliakseisavachkin during the Fall '08 term at University of South Florida.

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ch08 - CHAPTER 8 Section 8-2 8-7 a The 99 CI on the mean...

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