A random sample of size n from a normal population with

Question

Show that if μ_1 0 in Example 4, the Ney man- Pearson lemma yields the critical region

Example 4

A random sample of size n from a normal population with σ² = 1 is to be used to test the null hypothesis μ = μ₀against the alternative hypothesis μ = μ₁, where μ₁ > μ₀. Use the Ney man-Pearson lemma to find the most powerful critical region of size α.