tut_8_Chap_8_sol - CollegeofEngineering,QatarUniversity

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College of Engineering, Qatar University Page 1 of 5 Probability and Statistics, GENG200 2B Tutorial - 8 Question Sections 8-2 Page 267: 1) 8.3 Answer: 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. Quiestion: Section 8-2, Page 267 2) 8-4 Answer: 8-4 a) 95% CI for 96 . 1 , 1000 20 , 10 , = = = = z x n σ μ {P(z) = 1-0.025 = 0.975} 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 {P(z) = 1-0.005 = 0.995} 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.
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College of Engineering, Qatar University Page 2 of 5 Question Chapter 8: 1) 8-6 Answer: 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.
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tut_8_Chap_8_sol - CollegeofEngineering,QatarUniversity

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