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Let Y1, Y2, . . . , Y20 be a random sample of size n = 20 from a normal distribution with unknown mean µ and known variance σ 2 = 5. We want to test H0; µ = 7 vs. Ha : µ > 7. (a) Find the uniformly most powerful test with significance level 0.05. (b) For the test in (a), find the power at each of the following alternative values of µ: µa = 7.5, 8.0, 8.5, and 9.0. (c) Sketch a graph of the power function (d) What is the smallest sample size n such that an α = 0.05-level test has power at least 0.8 when µ = 8?

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orchestra answered 1 year ago

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