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Homework10Solutions

# Homework10Solutions - Steven Weber Dept of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Homework 10 Solutions (Monday, June 2) Question 1: #1, § 7.1, p262. Consider a normal population with the value of σ known. a. What is the confidence level for the interval ¯ x ± 2 . 81 σ/ n ? Φ(2 . 81) = 0 . 9975 1 - α/ 2 = 0 . 9975 1 - α = 0 . 995 . (1) b. What is the confidence level for the interval ¯ x ± 1 . 44 σ/ n ? Φ(1 . 44) = 0 . 9251 1 - α/ 2 = 0 . 9251 1 - α = 0 . 85 . (2) c. What value of z α/ 2 in the CI formula (7.5) results in a confidence level of 99 . 7% ? 1 - α = 0 . 997 1 - α/ 2 = 0 . 9985 Φ(2 . 97) = 0 . 9985 z α/ 2 = 2 . 97 . (3) d. Answer the question posed in part (c) for a confidence level of 75% . 1 - α = 0 . 75 1 - α/ 2 = 0 . 875 Φ(1 . 15) = 0 . 875 z α/ 2 = 1 . 15 . (4) Question 2: #3, § 7.1, p262. Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let μ denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.8,9.4).

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