Let $X_1, \dotsc, X_n$ be i.i.d. $N(\mu,\sigma^2)$, where $\sigma^2$ is known, but $\mu$ is unknown. Construct a two sided 95% CI for $\mu$ based on $X_1, \dotsc, X_n$?
I am unsure how to go about this problem when there is an unknown involved.
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1It doesn't make sense to speak of a confidence interval when there is not an unknown involved. – Michael Hardy Oct 29 '17 at 00:52
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First, pretend $n$ is 50 and $\sigma$ is 7. Figure out how to build the confidence interval from that. Then, go back and figure out what would be different if you had left the symbols in place all along. (Hint: very little would be different.) – Aaron Montgomery Oct 29 '17 at 00:59