Rejection Region vs P-Value

You fix $\alpha$ (alpha, the significance level) before collecting data, find the critical value cutting off area $\alpha$ in the tail or tails, and everything beyond it makes up the rejection region. For a two-sided z-test at $\alpha = 0.05$ the region is $|z| \geq 1.96$, while a one-sided test at the same alpha uses $z \geq 1.645$ (or $z \leq -1.645$ for a left-tailed alternative), because all 5% sits in one tail. The Fall 2026 AP course frames the decision as comparing the p-value to alpha rather than drawing a region, so you will rarely need to sketch one. Both routes give the same verdict, since a test statistic lands in the rejection region exactly when its p-value is at or below alpha.

A p-value measures how well your data agree with the null hypothesis: a small p-value means the observed result would be surprising if the null were true, which counts as evidence against it. It is a probability about the data, not the probability that the null hypothesis is true. For example, a p-value of 0.02 says that if the null hypothesis held, data at least this extreme would occur about 2% of the time. You reject the null hypothesis when the p-value is at or below the significance level $\alpha$ (the Greek letter alpha).