Although the use of simulation to teach the sampling distribution of the mean is meant to provide
students with sound conceptual understanding, it may lead them astray. We discuss a
misunderstanding that can be introduced or reinforced when students who intuitively understand
that “bigger samples are better” conduct a simulation to explore the effect of sample size on the
properties of the sampling distribution of the mean. From observing the patterns in a typical
series of simulated sampling distributions constructed with increasing sample sizes, students
reasonably—but incorrectly—conclude that, as the sample size, n, increases, the mean of the
(exact) sampling distribution tends to get closer to the population mean and its variance tends to
get closer to ????2/n, where ????2 is the population variance. We show that the patterns students
observe are a consequence of the fact that both the variability in the mean and the variability in
the variance of simulated sampling distributions constructed from the means of N random
samples are inversely related, not only to N, but also to the size of each sample, n. Further,
asking students to increase the number of repetitions, N, in the simulation does not change the
patterns
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education