Suppose that a random sample from a normal popula-tion with the known variance σ2 is to be used to test the null hypothesis μ = μ0 against the alternative hypothe-sis μ = μ1, where μ1 > μ0, and that the probabilities of type I and type II errors are to have the preassigned val-ues α and β. Show that the required size of the sample is given by n = σ2(zα + zβ)2(μ1 − μ0)2

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