Chapter 10.10, Problem 94E

Suppose that Y₁, Y₂, … ,Y_n constitute a random sample from a normal distribution with known mean μ and unknown variance σ². Find the most powerful α-level test of $H_0:{\sigma }^2={\sigma }_0^2$ versus $H_a:{\sigma }^2={\sigma }_1^2$, where ${\sigma }_1^2>{\sigma }_0^2$. Show that this test is equivalent to a χ² test. Is the test uniformly most powerful for $H_a:{\sigma }^2>{\sigma }_0^2$?