Reject $H_0$ in favor of $H_1$ if $\bar X_1 - \bar X_2 > z_{\alpha/2} \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$ or $\bar X_1 - \bar X_2 < -z_{\alpha/2} \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}$