A rejection region contains test-statistic values whose probability under H_0 is at most the chosen significance level. Signed critical values must agree with the alternative hypothesis. Left-tailed critical region Right-tailed critical region Two-tailed critical regions Observed value in left tail Observed value in right tail Observed value in either tail **Alternative** | **Reject H_0 when** H_1:mu< _0 | z_ obs <= z_alpha, where z_alpha<0 and P(Z <= z_alpha)=alpha H_1:mu> _0 | z_ obs >= z_1-alpha, where z_1-alpha>0 H_1:mu!= _0 | |z_ obs| >= z_1-alpha/2

A rejection region contains test-statistic values whose probability under \(H_0\) is at most the chosen significance level. Signed critical values must agree with the alternative hypothesis.

Alternative	Reject \(H_0\) when
\(H_1:\mu<\mu_0\)	\(z_{\rm obs}\leq z_\alpha\), where \(z_\alpha<0\) and \(P(Z\leq z_\alpha)=\alpha\)
\(H_1:\mu>\mu_0\)	\(z_{\rm obs}\geq z_{1-\alpha}\), where \(z_{1-\alpha}>0\)
\(H_1:\mu\ne\mu_0\)	\(\|z_{\rm obs}\|\geq z_{1-\alpha/2}\)

Rejection Regions and Critical Values

Rejection Regions and Critical Values