State Wilks' Theorem on the asymptotic distribution of likelihood-ratio test statistics.

Suppose that $X_{1}, \ldots, X_{n}$ are independent with common $N\left(\mu, \sigma^{2}\right)$ distribution, where the parameters $\mu$ and $\sigma$ are both unknown. Find the likelihood-ratio test statistic for testing $H_{0}: \mu=0$ against $H_{1}: \mu$ unrestricted, and state its (approximate) distribution.

What is the form of the $t$-test of $H_{0}$ against $H_{1}$ ? Explain why for large $n$ the likelihood-ratio test and the $t$-test are nearly the same.