AP Statistics Unit 5: Sampling Distributions

A statistic such as $\hat{p}$ or $\bar{x}$ varies from sample to sample. Its sampling distribution describes that variation and is the foundation of every confidence interval and significance test in the course.

For a sample proportion, the mean is $p$ and the standard deviation is $\sqrt{p(1-p)/n}$; the shape is approximately normal when $np \ge 10$ and $n(1-p) \ge 10$. For a sample mean, the mean is $\mu$ and the standard deviation is $\sigma/\sqrt{n}$; the Central Limit Theorem says the shape is approximately normal for large $n$ even when the population is skewed. The 10% condition, $n \le 0.1N$, justifies these formulas when sampling without replacement.