AP Statistics · Summary

Unit 4 summary

1. For a mean, use s and the t distribution: $\bar{x} \pm t^* \frac{s}{\sqrt{n}}$ with df = n - 1.
2. Check Random, 10% and Normal/Large Sample. With n under 30, look at the data for strong skew or outliers.
3. Interpret an interval as C% confidence that it captures the population mean in context, never as the range of individual values.
4. Hypotheses are about $\mu$. Compute $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$, find the p-value in the direction of $H_a$, and compare it with $\alpha$.
5. A p-value assumes $H_0$ is true. Failing to reject is not evidence that $H_0$ is true.
6. Same units measured twice or matched pairs: paired t on the differences, df = pairs minus 1. Separate groups: two-sample t with $\sqrt{s_1^2/n_1 + s_2^2/n_2}$.
7. A value inside a C% interval is plausible; a two-sided test at $\alpha = 1 - C$ on the same data will not reject it.