题目

设总体 X sim N(mu, sigma^2)，sigma^2 未知，overline(X) 为样本均值，S_n^2 = (1)/(n) sum_(i=1)^n (X_i - overline(X))^2，S^2 = (1)/(n-1) sum_(i=1)^n (X_i - overline(X))^2，检验假设 H_0: mu = mu_0 时采用的统计量是A. Z = (overline(X) - mu_0)/(sigma / sqrt(n))B. T = (overline(X) - mu_0)/(S_n / sqrt(n))C. T = (overline(X) - mu_0)/(sigma / sqrt(n))D. T = (overline(X) - mu_0)/(S / sqrt(n))

设总体 $X \sim N(\mu, \sigma^2)$，$\sigma^2$ 未知，$\overline{X}$ 为样本均值，$S_n^2 = \frac{1}{n} \sum_{i=1}^n (X_i - \overline{X})^2$，$S^2 = \frac{1}{n-1} \sum_{i=1}^n (X_i - \overline{X})^2$，检验假设 $H_0: \mu = \mu_0$ 时采用的统计量是

A. $Z = \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$

B. $T = \frac{\overline{X} - \mu_0}{S_n / \sqrt{n}}$

C. $T = \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$

D. $T = \frac{\overline{X} - \mu_0}{S / \sqrt{n}}$

题目解答

答案

D. $T = \frac{\overline{X} - \mu_0}{S / \sqrt{n}}$