Suppose that independent random samples of size nfrom two normal populations with the known variancesσ21 and σ22 are to be used to test the null hypothesis μ1 −μ2 = δ against the alternative hypothesis μ1 − μ2 = δand that the probabilities of type I and type II errors areto have the preassigned values α and β. Show that therequired size of the sample is given by n = (σ21 + σ22 )(zα + zβ)2(δ − δ)2

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