\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016f.01283}
\itemau{Watkins, Ann E.; Bargagliotti, Anna; Franklin, Christine}
\itemti{Simulation of the sampling distribution of the mean can mislead.}
\itemso{J. Stat. Educ. 22, No. 3, 21 p., electronic only (2014).}
\itemab
Summary: 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 ${\sigma}^2$/$n$, where ${\sigma}^2$ 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.
\itemrv{~}
\itemcc{K70 K90}
\itemut{stochastics; sampling distribution of the mean; simulation; sampling variability; variance of means; variance of variances; central limit theorem; estimated mean; estimated standard deviation}
\itemli{http://ww2.amstat.org/publications/jse/v22n3/watkins.pdf}
\end