Suppose $X_{1}, \ldots, X_{n}$ are independent $N\left(0, \sigma^{2}\right)$ random variables, where $\sigma^{2}$ is an unknown parameter. Explain carefully how to construct the uniformly most powerful test of size $\alpha$ for the hypothesis $H_{0}: \sigma^{2}=1$ versus the alternative $H_{1}: \sigma^{2}>1$.