题目
8.设Xsim N(mu,sigma^2)，mu,sigma^2均未知，若样本容量为n，sigma^2的95%的置信区间为（）.A. [((n-1)S^2)/(x_(0.975)^2(n-1)),((n-1)S^2)/(x_(0.025)^2(n-1))]B. [((n-1)S^2)/(x_(0.025)^2(n-1)),((n-1)S^2)/(x_(0.975)^2(n-1))]C. [((n-1)S^2)/(t_(0.025)^2(n-1)),((n-1)S^2)/(t_(0.975)^2(n-1))]D. [overline(x)pm(S)/(sqrt(n))t_(0.025)(n-1)]
8.设$X\sim N(\mu,\sigma^{2})$，$\mu,\sigma^{2}$均未知，若样本容量为n，$\sigma^{2}$的95%的置信区间为（）.
A. $\left[\frac{(n-1)S^{2}}{x_{0.975}^{2}(n-1)},\frac{(n-1)S^{2}}{x_{0.025}^{2}(n-1)}\right]$
B. $\left[\frac{(n-1)S^{2}}{x_{0.025}^{2}(n-1)},\frac{(n-1)S^{2}}{x_{0.975}^{2}(n-1)}\right]$
C. $\left[\frac{(n-1)S^{2}}{t_{0.025}^{2}(n-1)},\frac{(n-1)S^{2}}{t_{0.975}^{2}(n-1)}\right]$
D. $\left[\overline{x}\pm\frac{S}{\sqrt{n}}t_{0.025}(n-1)\right]$
题目解答
答案
B. $\left[\frac{(n-1)S^{2}}{x_{0.025}^{2}(n-1)},\frac{(n-1)S^{2}}{x_{0.975}^{2}(n-1)}\right]$