Unit 5: Sampling Distributions
AP Statistics: 52 practice questions with detailed explanations.
Unit Study Guide
Executive Summary
A statistic varies from sample to sample. Its sampling distribution tells us how close estimates land to the parameter.
Parameters vs statistics
A parameter describes a population (fixed); a statistic describes a sample (varies). Sampling distributions are built from many samples of the same size. Bias = center off the parameter; variability = spread across samples. Good estimators are unbiased with low variability.
Proportions
The sampling distribution of p-hat has mean p and standard deviation √(p(1-p)/n). It's approximately normal when np and n(1-p) are both at least 10 (large counts) and the sample is at most 10% of the population.
Means
The sampling distribution of x-bar has mean μ and standard deviation σ / √(n) — averaging reduces spread. If the population is normal, x-bar is normal for any n; otherwise the Central Limit Theorem says x-bar is approximately normal for n at least 30.
Key ideas
Bigger n → smaller standard error (scales as 1/√(n)). To halve the standard error, quadruple n. Sample mean and sample proportion are unbiased; the sample range underestimates the population range.
Exam traps
Standard error shrinks with n, but the population doesn't change. The CLT is about sample MEANS, not individual values. Bias comes from the estimator's center, not its spread.