2007-66.md

course	course_year	question_number	tags	title	year
Statistics	IB	66	IB 2007 Statistics	1.I.7C	2007

Let $X_{1}, \ldots, X_{n}$ be independent, identically distributed random variables from the $N\left(\mu, \sigma^{2}\right)$ distribution where $\mu$ and $\sigma^{2}$ are unknown. Use the generalized likelihood-ratio test to derive the form of a test of the hypothesis $H_{0}: \mu=\mu_{0}$ against $H_{1}: \mu \neq \mu_{0}$.

Explain carefully how the test should be implemented.