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What is the power to detect a shift to 108?

A quality engineer tests H0:μ=100H_0: \mu = 100 against H1:μ>100H_1: \mu > 100 with a known σ=15\sigma = 15, a sample of n=25n = 25, at the one-sided 5% level. Suppose the process has actually shifted to a true mean of μ=108\mu = 108.

Find the power of the test (the probability it correctly rejects H0H_0) and the Type II error rate β\beta.

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