# Question

Suppose that independent random samples of size n from two normal populations with the known variances σ21 and σ22 are to be used to test the null hypothesis µ1 – µ2 = ∂t against the alternative hypothesis µ1 – µ2 = d and that the probabilities of type I and type II errors are to have the preassigned values a and β. Show that the required size of the sample is given by

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