A Sample/Population Size Activity: Is it the sample size of the sample as a fraction of the population that matters?

Abstract

Unless the sample encompasses a substantial portion of the population, the standard error of an estimator depends on the size of the sample, but not the size of the population. This is a crucial statistical insight that students find very counterintuitive. After trying several ways of convincing students of the validity of this principle, I have finally found a simple memorable activity that convinces students beyond a reasonable doubt. As a bonus, the data generated by this activity can be used to illustrate the central limit theorem, confidence intervals, and hypothesis testing.

Supplemental data for this article can be accessed on the publisher's website.

• Sample size
• Sampling distribution
• Standard error

Acknowledgements

The author would like to thank the editor and referees for their very helpful comments and suggestions.