AP Statistics · Summary

Unit 3 summary

1. A confidence interval is estimate plus or minus critical value times standard error; interpret it as capturing the population parameter, in context, and the level as the method's long-run capture rate.
2. For a test, write hypotheses about the parameter, check conditions with the null value, find the P-value in the direction of $H_a$, and compare it with alpha.
3. Conclude with "convincing evidence" or "not convincing evidence" for $H_a$, in context; never accept $H_0$ or claim proof.
4. A Type I error rejects a true $H_0$ (probability alpha); a Type II error misses a true $H_a$. Power is 1 minus the chance of a Type II error, and it rises with n, alpha and the distance from the null value.
5. For two proportions, use the unpooled standard error for an interval and the pooled proportion for a test of equal proportions; an interval that contains 0 does not show a difference.
6. Chi-square tests use counts: expected count is row total times column total over the grand total, df = (r - 1)(c - 1), and every expected count should be at least 5.
7. Use homogeneity for separate samples or groups compared on one variable, and independence for one sample classified by two variables.