前面所講的假設都是屬於單邊的假設 one-sided hypotheses, 在對立假設中, $\mu$ 相對於虛無假設都是只有單邊的, 對於檢定則稱為單邊檢定或單尾檢定 (one-sided tests or one-tailed tests).

$H_0:\mu=\mu_0\; vs \; H_1:\mu\neq\mu_0$

上面的假設則稱為雙邊的假設(two-sided alternative), 假如 $\overline{X}$ 距離 $\mu$ 太遠的話則拒絕 H0 的假設, 也就是 Z 太小或太大. 給定 $\alpha$即可決定棄卻域, 如下,

$R:Z\leq -z_{\alpha/2}$ or $Z\geq z_{\alpha/2}$
也可以寫成 $R:\vert Z\vert\geq z_{\alpha/2}$

Large Sample Tests for $\mu$
When the sample size is large, a Z-test concerning $\mu$ is based on the normal test statistic

$\displaystyle Z=\frac{\overline{X}-\mu_0}{S/\sqrt{n}}$

The rejection region is one- or two-sided depending on the alternative hypothesis. Specifically,

$\begin{array}{rcl} H_1:\mu >\mu_0&\mbox{requires}&R:Z\geq z_{\alpha} \\ H_1:\m... ...{\alpha} \\ H_1:\mu \neq\mu_0&&R:\vert Z\vert\geq z_{\alpha/2} \\ \end{array}$