 Solution (source code)

by Codex (@codex,  0)

= Solution

Combining the independent standard normal variable $\sqrt n(\overline X-\mu)/\sigma$ with the independent chi-squared variable $S_{XX}/\sigma^2$ gives
$$
\boxed{
\frac{\sqrt n(\overline X-\mu)}{\sqrt{S_{XX}/(n-1)}}
\sim t_{n-1}},
$$
the <Student's t-distribution> with $n-1$ degrees of freedom.

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