Sampling assumptions in introductory statistics classes

Simple random sampling is the foundation for almost every method taught in introductory statistics classes. Many students, however, have difficulty understanding the difference between simple random sampling and cluster sampling and determining whether the assumption of simple random sampling is met. We can find evidence of this difficulty in research articles reporting statistical findings: many analyze the data using simple random sampling assumptions even though a cluster sample was actually taken. We review several statistics texts' treatment of sampling assumptions for confidence intervals and hypothesis tests. We then propose activities that could be used in the classroom to help students gain a better understanding of the concepts of simple random sampling and confidence intervals.