I have a $X_1, \cdots , X_n$ random samples from a $N(\mu,\sigma^2)$. $\mu$ is known, but $\sigma^2$ is unknown. I would like to know how to go about constructing a $(1-\alpha)$100% shortest confidence interval for $\sigma^2$.
I know how how to construct that of a known variance, but unknown mean. I'm bit confused as how to proceed when the situation is reversed.
Thank you.