表 8.2 单个正态总体方差的假设检验的拒绝域

单个正态总体方差 ${\sigma }^2$ 的假设检验的拒绝域 (显著性水平为 $\alpha$ )

序号	$H_0$	$H_1$	$\mu$ 已知	$\mu$ 未知
I	${\sigma }^2={\sigma }_0^2$	${\sigma }^2\ne {\sigma }_0^2$	$\frac{\sum _{i=1}^n{\left(x_i-\mu \right)}^2}{{\sigma }_0^2}\le {\chi }_{\frac{\alpha }{2}}^2\left(n\right)$ 或 $\frac{\sum _{i=1}^n{\left(x_i-\mu \right)}^2}{{\sigma }_0^2}\ge {\chi }_{1-\alpha }^2\left(n\right)$	$\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{{\sigma }_0^2}\le {\chi }_{\alpha /2}^2\left(n-1\right)$ 或 $\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{{\sigma }_0^2}\ge {\chi }_{1-\alpha /2}^2\left(n-1\right)$
II	${\sigma }^2={\sigma }_0^2$	${\sigma }^2>{\sigma }_0^2$	$\frac{\sum _{i=1}^n{\left(x_i-\mu \right)}^2}{{\sigma }_0^2}\ge {\chi }_{1-\alpha }^2\left(n\right)$	$\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{{\sigma }_0^2}\ge {\chi }_{1-\alpha }^2\left(n-1\right)$
III	${\sigma }^2\le {\sigma }_0^2$	${\sigma }^2>{\sigma }_0^2$	同 II	同 II
IV	${\sigma }^2={\sigma }_0^2$	${\sigma }^2<{\sigma }_0^2$	$\frac{\sum _{i=1}^n{\left(x_i-\mu \right)}^2}{{\sigma }_0^2}\le \lambda$	$\frac{\sum _{i=1}^n{\left(x_i-\bar{x}\right)}^2}{{\sigma }_0^2}\le {\chi }_{\alpha }^2\left(n-1\right)$
V	${\sigma }^2\ge {\sigma }_0^2$	${\sigma }^2<{\sigma }_0^2$	同 IV	同 IV