ch08.docx

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Applied Statistics and Probability for Engineers, 5 th edition September 22, 2010 CHAPTER 8 Section 8-1 8-1 a) The confidence level for ¯ x2.14 σ / nμ≤¯ x+2.14σ / n is determined by the value of z0 which is 2.14. From Table III, (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 ¯ x2.49 σ / nμ≤¯ x+ 2.49 σ / n is determined by the by the value of z0 which is 2.14. From Table III, (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 ¯ x1.85 σ / nμ≤¯ x+1.85σ / n is determined by the by the value of z0 which is 2.14. From Table III, (1.85) = P(Z<1.85) = 0.9678 and the confidence level is 93.56%. 8-2 a) A z = 2.33 would give result in a 98% two-sided confidence interval. b) A z = 1.29 would give result in a 80% two-sided confidence interval. c) A z = 1.15 would give result in a 75% two-sided confidence interval. 8-3 a) A z = 1.29 would give result in a 90% one-sided confidence interval. b) A z = 1.65 would give result in a 95% one-sided confidence interval. c) A z = 2.33 would give result in a 99% one-sided confidence interval. 8-4 a) 95% CI for μ, n=10 =20 ¯ x=1000 ,z=1.96 ¯ x/ nμ≤¯ x +/ n 10001.96( 20/ 10)≤μ1000+ 1.96 ( 20/ 10 ) 987.6μ1012.4 b) .95% CI for μ, n=25 =20 ¯ x=1000 ,z=1.96 ¯ x/ nμ≤¯ x +/ n 10001.96( 20/ 25)≤μ1000+ 1.96( 20/ 25) 992.2μ1007.8 c) 99% CI for μ, n=10 =20 ¯ x=1000 ,z=2.58 ¯ x/ nμ≤¯ x +/ n 10002.58( 20/ 10)≤μ1000+ 2.58( 20/ 10) 983.7μ1016.3 d) 99% CI for μ, n=25 =20 ¯ x=1000 ,z=2.58 ¯ x/ nμ≤¯ x +/ n 10002.58( 20 / 25 )≤μ1000+ 2.58( 20/ 25) 989.7μ1010.3 e) When n is larger, the CI is narrower. The higher the confidence level, the wider the CI. 8-1

Transcript of ch08.docx

CHAPTER 8

Applied Statistics and Probability for Engineers, 5th editionSeptember 22, 2010

CHAPTER 8

Section 8-1

8-1

a) The confidence level for is determined by the

value of z0 which is 2.14. 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