Section 9.3 Summary

1. The $p$-value can be thought of as the probability of observing a sample statistic at least as extreme as the statistic in your sample if we assume that the null hypothesis is true. The rejection rule for the $p$-value method is to reject $H_0$ when the $\text{p-value}\le \alpha$, the level of significance.
2. The $p$-value can be used to assess the strength of evidence against the null hypothesis.
3. The critical-value method and the $p$-value method are equivalent, and related in several ways.
4. We can use a single confidence interval for $\mu$ to help us perform any number of corresponding two-tailed hypothesis tests about $\mu$.