One-Sided Test vs Two-Sided Test

You choose the direction before you look at the data, based on the claim being investigated, and the p-value is then the area in that single tail of the null distribution. In AP Statistics the null hypothesis is tested at the boundary of equality even when the alternative points one way. For example, with $H_a: p > 0.50$ and a test statistic of $z = 1.75$, the p-value is $P(Z > 1.75) = 0.0401$. A one-sided test detects a given effect more easily than a two-sided test, but only when the effect runs in the hypothesized direction, which is exactly why picking the direction after seeing the data is cheating.

Use a two-sided alternative when you want to detect any change rather than a change in a specific direction, which fits most research questions. Because both tails count, the p-value is twice the one-tail area whenever the null distribution is symmetric. For example, a test statistic of $z = 1.75$ gives a p-value of $2 \times 0.0401 = 0.0802$, against 0.0401 for the matching one-sided test. A two-sided test at $\alpha = 0.05$ (alpha, the significance level) usually agrees with the 95% confidence interval, though for proportions the two can disagree in close cases because they use different standard errors.