设 $X_1, X_2, \cdots, X_n$ 是来自正态总体 $N\left(\mu, \sigma^2\right)$ 的简单随机样本， $\bar{X}$ 是样本均值，记
$$
\begin{aligned}
& S_1^2=\frac{1}{n-1} \sum_{i=1}^n\left(X_i-\bar{X}\right)^2, S_2^2=\frac{1}{n} \sum_{i=1}^n\left(X_i-\bar{X}\right)^2 \\
& S_3^2=\frac{1}{n-1} \sum_{i=1}^n\left(X_i-\mu\right)^2, S_4^2=\frac{1}{n} \sum_{i=1}^n\left(X_i-\mu\right)^2
\end{aligned}
$$
则服从自由度为 $n-1$ 的 $t$ 分布的随机变量是
$\text{A.}$ $t=\frac{\bar{X}-\mu}{S_1 / \sqrt{n-1}}$
$\text{B.}$ $t=\frac{\bar{X}-\mu}{S_2 / \sqrt{n-1}}$
$\text{C.}$ $t=\frac{\bar{X}-\mu}{S_3 / \sqrt{n}}$
$\text{D.}$ $t=\frac{\bar{X}-\mu}{S_4 / \sqrt{n}}$