数学试题讲解

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设

X_{1}, X_{2}, \dots, X_{n}

是来自正态总体

N (μ, σ^{2})

的简单随机样本,

\bar{X}

是样本均值, 记

\begin{array}{ll} S_{1}^{2} = \frac{1}{n - 1} \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}, & S_{2}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}, \\ S_{3}^{2} = \frac{1}{n - 1} \sum_{i = 1}^{n} {(X_{i} - μ)}^{2}, & S_{k}^{2} = \frac{1}{n} \sum_{i = 1}^{n} {(X_{i} - μ)}^{2}, \end{array}

则服从自由度为

n - 1

的

t

分布的随机变量是

A.

t = \frac{\bar{X} - μ}{S_{1} / \sqrt{n - 1}}

. B.

t = \frac{\bar{X} - μ}{S_{2} / \sqrt{n - 1}}

. C.

t = \frac{\bar{X} - μ}{S_{3} / \sqrt{n}}

. D.

t = \frac{\bar{X} - μ}{S_{4} / \sqrt{n}}

.