= Studentized sample mean
{title2=$T_n=\sqrt n(\overline X-\mu)/S$}
For <independent and identically distributed> observations with finite positive <variance>, the <central limit theorem>, consistency of the <sample variance> and <Slutsky's theorem> give $T_n\xrightarrow{d}N(0,1)$. Under an independent <normal distribution> sample it instead has the exact finite-sample <Student t-distribution> with $n-1$ degrees of freedom, as described by the <studentized normal sample mean>. The asymptotic statement does not require normal individual observations.
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