Sampling distributions, simulation and the central limit theorem

Learning objectives

Distinguish the distribution of a population, the distribution of one sample and the sampling distribution of a statistic, and explain that a sampling distribution describes the values a statistic takes over all possible samples of the same size

Describe how to approximate a sampling distribution by simulation — repeatedly take a random sample of a fixed size, calculate the statistic and record it — and describe the center, variability and shape of the simulated distribution from a dotplot or histogram

Describe how a randomization distribution is built — shuffle the observed responses at random into groups of the original sizes, work out the statistic, and repeat many times — and explain what the distribution represents

Use a simulated sampling distribution or a randomization distribution to estimate how often a value at least as extreme as the observed statistic would occur by chance alone, and judge whether the observed result is surprising

State the central limit theorem — the sampling distribution of a sample mean is approximately normal when the sample size is large, and closer to normal the larger the sample — and explain that it describes the statistic, not the population or the data in one sample