# ** Sampling Distribution of the Mean Tutorial

This tutorial demonstrates the properties of sampling distributions using a Java applet. The tutorial has an accompanying hand-out that you can download.
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Date Of Record Creation 2004-03-10 13:30:00 2010-04-07 11:46:00 2004-07-27 10:45:00 http://wise.cgu.edu/ dale.berger@cgu.edu Dale Berger Claremont Graduate University, Claremont, CA Java capable browser The content is restricted to one aspect of the relationship between sample size and sampling distributions: variability. However, there are at least two other aspects that are very important: shape and center. These aspects will be helpful to understand in order to completely and correctly answer the questions in the tutorial that ask for comparisons of sampling distributions for different sample sizes. The tutorial starts with samples of 100 and then works down to smaller sample sizes. This is the opposite order of what an instructor would typically use. This order might be OK, but something rather important is missing: the student is not encouraged to try samples of size n=1. Indeed, the applet does not support n=1. A detailed tutorial that includes an applet that visually displays the sampling distribution of a sample mean. The size of the text and the graphics of the applet can be quite small on many screens and may be difficult to read. This could be especially problematic if demonstrating the applet for students is on a classroom projector. The tutorial and applet have clear instructions and are easy to use. A primary concern is that there is no option available to overlay the sampling distributions for different sample sizes. Such an option would be powerful in helping students make the desired connection. As it currently is, students must remember what the previous sampling distribution looked like. Also, it would be good to include questions that ask for the explicit calculation of the standard deviation of the sampling distribution. Another primary concern is that the applet is hard-wired to one very specific context or example. Teachers aren't able to use different initial values for the mean and standard deviation which limits this tutorial's effectiveness. Also, students only have a few sample size options to select from. Finally, the tutorial and applet assume the population is normally distributed which is often not valid when collecting real data. The directions are explicit and clear. A student should be able to use the applet quite easily. The step-by-step questions build on one another and are designed to help the student see the connection between sample size and variability in the sampling distribution. The applet allows for an overlay of the sample data, the sampling distribution, and the population distribution. 4 4 3 1