두 표본 Z검정 (Two Sample Z Test)

$$\sigma_{1}^{2}$$ 과&nbsp&nbsp $$\sigma_{2}^{2}$$ 을 알 때

• 귀무가설
  • $$H_{0} : \mu_{1} = \mu_{2}$$

• 검정통계량
  • $$Z_{0} = \frac{\overline{X} - \overline{Y}}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}} + \frac{\sigma_{2}^{2}}{n_{2}}}}$$

• 대립가설과 기각역
  • $$ H_{1} : \mu_{1} > \mu_{2} \ \rightarrow \ z_{0} > z_{\alpha} $$
  • $$ H_{1} : \mu_{1} < \mu_{2} \ \rightarrow \ z_{0} < - z_{\alpha} $$
  • $$ H_{1} : \mu_{1} \neq \mu_{2} \ \rightarrow \ | \ z_{0} \ | > z_{\alpha/2} $$

• 검정