Solution
= Solution
\b[Yes, it is a <uniformly most powerful test> for the one-sided alternative.] For every fixed $\sigma_1^2>\sigma_0^2$, the likelihood ratio is increasing in the same statistic $S$. The size-$\alpha$ threshold found in part (c) depends only on the null <variance> and $\alpha$, not on the selected alternative <variance>. Thus one and the same test is most powerful against each simple member of the composite alternative, which is exactly uniform most powerfulness.