表 8.3 两个独立正态总体均值差的假设检验的拒绝域

两个独立正态总体均值差的假设检验的拒绝域 (显著性水平为 $α$ )

序号	$H_{0}$	$H_{1}$	$σ_{1}^{2}, σ_{2}^{2}$ 已知	$σ_{1}^{2} = σ_{2}^{2}$ 未知
I	$μ_{1} - μ_{2} = δ$	$μ_{1} - μ_{2} \neq = δ$	$\frac{∣ ( x ˉ - y ˉ ) - δ ∣}{\frac{σ _{1}^{2}}{m} + \frac{σ _{2}^{2}}{n}} \geq u_{1 - \frac{α}{2}}$	$\frac{∣ ( x ˉ - y ˉ ) - δ ∣}{S _{w} \frac{1}{m} + \frac{1}{n}} \geq t_{1 - \frac{α}{2}} (m + n - 2)$
II	$μ_{1} - μ_{2} = δ$	$μ_{1} - μ_{2} > δ$	$\frac{( x ˉ - y ˉ ) - δ}{\frac{σ _{1}^{2}}{m} + \frac{σ _{2}^{2}}{n}} \geq u_{1 - α}$	$\frac{( x ˉ - y ˉ ) - δ}{S _{w} \frac{1}{m} + \frac{1}{n}} \geq t_{1 - α} (m + n - 2)$
III	$μ_{1} - μ_{2} \leq δ$	$μ_{1} - μ_{2} > δ$	同 II	同 II
IV	$μ_{1} - μ_{2} = δ$	$μ_{1} - μ_{2} < δ$	$\frac{( x ˉ - y ˉ ) - δ}{\frac{σ _{1}^{2}}{m} + \frac{σ _{2}^{2}}{n}} \leq u_{α}$	$\frac{( x ˉ - y ˉ ) - δ}{S _{w} \frac{1}{m} + \frac{1}{n}} \leq t_{α} (m + n - 2)$
V	$μ_{1} - μ_{2} \geq δ$	$μ_{1} - μ_{2} < δ$	同 IV	同 IV

Youliang Zhong