Section 9.2 Summary

1. The essential idea about hypothesis testing for the mean is as follows: When the observed value of $\overline{x}$ is unusual or extreme in the sampling distribution of $\overline{x}$ that assumes $H_0$ is true, we should reject $H_0$. Otherwise, we should not reject $H_0$.
2. The test statistic $Z_{\text{data}}$ summarizes the information in the data set regarding the hypothesis test.
3. The critical region consists of the range of values of the test statistic $Z_{\text{data}}$ for which we reject the null hypothesis. The value of $Z$ that separates the critical region from the noncritical region is called the critical value $Z_{\text{crit}}$.
4. In the critical-value method for the $Z$ test for the mean, we compare $Z_{\text{data}}$ with $Z_{\text{crit}}$.