Chapter 10.11, Problem 105E

Let Y₁, Y₂,…, Y_n denote a random sample from a normal distribution with mean μ (unknown) and variance σ². For testing $H_0:{\sigma }^2={\sigma }_0^2$ against $H_a:{\sigma }^2={\sigma }_0^2$, show that the likelihood ratio test is equivalent to the χ² test given in Section 10.9.