Suppose that independent random samples of size n from two normal populations with the known variances σ₁² and σ₂² are to be used to test the null hypothesis μ₁ - μ₂ = δ₀ against the alternative hypothesis μ₁ - μ₂ = δₐ. Suppose further that the probabilities of type I and type II errors are to have the preassigned values α and β.
Show that the required size of the sample is given by