Let us say the life of a tire in miles, say X, is normally distributed with mean

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Let us say the life of a tire in miles, say X, is normally distributed with mean θ and standard deviation 5000. Past experience indicates that θ = 30,000. The manufacturer claims that the tires made by a new process have mean θ > 30,000. It is possible that θ = 35,000. Check his claim by testing H0 : θ = 30,000 against H1 : θ > 30,000. We observe n independent values of X, say x1, . . . , xn, and we reject H0 (thus accept H1) if and only if ¯x ≥ c. Determine n and c so that the power function ϒ(θ) of the test has the values ϒ(30,000) = 0.01 and ϒ(35,000) = 0.98.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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