Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 8, Problem 79SE
Let X1, X2,… Xn be a random sample from an exponential distribution with parameter λ. Then it can be shown that 2λΣXi has a chi-squared distribution with v = 2n (by first showing that 2λXi has a chi-squared distribution with v = 2).
- a. Use this fact to obtain a test statistic for testing H0: μ = μ0. Then explain how you would determine the P-value when the alternative hypothesis is Ha: μ < μ0. [Hint: E(Xi) = μ = 1/λ. So μ = μ0. equivalent to λ = 1/μ0.]
- b. Suppose that ten identical components, each having exponentially distributed time until failure, are tested. The resulting failure times are
- c. Use the test procedure of part (a) to decide whether the data strongly suggests that the true average lifetime is less than the previously claimed value of 75. [Hint: Consult Table A.7.]
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Chapter 8 Solutions
Probability and Statistics for Engineering and the Sciences
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