The AP Statistics exam expects you to choose the right inference procedure for each situation. Here's a decision framework that works every time.
Step 1: What type of data? Categorical data uses proportions and chi-square tests. Quantitative data uses means and t-tests. If you're looking at a relationship between two quantitative variables, think regression.
Step 2: How many groups? One sample: use a one-sample z-test (proportion) or one-sample t-test (mean). Two samples: use a two-sample z-test or two-sample t-test. Paired data: use a paired t-test.
Step 3: Chi-square tests. Goodness of fit: one categorical variable, testing if observed frequencies match expected. Test of independence: two categorical variables, testing association. Homogeneity: comparing distributions across populations.
Step 4: Regression. Use a t-test for the slope of a regression line to determine if there's a significant linear relationship. Check residual plots before concluding.
On the AP exam: Always state hypotheses, check conditions (random, normal, independent), calculate the test statistic, find the p-value, and make a conclusion in context. Missing any of these steps costs points on FRQs.