Data Matters with Fathom! Dynamic Statistics™ software

Activity 2.3

Section 2.3 makes some strong claims about the specifics of the bell curves that samples’ proportions fall into. It says that you can calculate something called the standard error with this equation:

This section also says that if you collect a lot of random samples and sort them from the smallest proportion to the largest, you will see this pattern.

• About 2.5% will be more than two standard errors below the probability.
• About 16% will be more than one standard error below the probability.
• About 50% will be below and about 50% will be above the probability.
• About 16% will be more than one standard error above the probability, so about 67% will be within one standard error of the probability.
• About 2.5% will be more than two standard errors above the probability, so about 95% will be within two standard errors of the probability and about 5% will be more than two standard errors away from the probability.

That’s a lot of claims. In this project, you will check these claims to see where they hold up and where they don’t. You are going to collect the same sorts of proportions you collected in Section 2.2. You will then sort them and work your way up, checking each of the claims.

Pick your probability and sample size. Before you proceed, calculate the standard error and find what you get when you add and subtract one and two standard errors from your probability.

Follow the same steps as in Section 2.2. Set the probability by changing the number of Yes’s and No’s. Set the sample size by using the Collection Inspector on the Sample Collection and setting the number of cases.

Set the number of samples to 1,000 by inspecting the Measures Collection and setting Measures to 1,000. With animation, that takes a long time, so as you’re setting it up, in every Collection Inspector click on the X next to Animation on to turn off the animation.

Once you have your Measures Collection with the proportions in it, right-click on the name of the proportions and select Sort Ascending. Now you can scroll through to check whether the predictions were supported.

Try other sample sizes and other probabilities. What samples sizes and/or proportions cause trouble for the claims about where the samples’ proportions fall? What kinds of trouble do they cause? Try other numbers of samples, such as 10. Does that cause trouble?