## Follow-up

We promised early in the lab to convince you that some of the initial assumptions we made about our "finite population" wouldn't impact the conclusions very much. Let's explore that claim.

- Select the
**Sleep 2**population in the applet. - Generate a distribution of 1,000 sample means, of the same size, from this population
- Use this new null distribution to approximate a simulation-based p-value and a theory-based p-value.
- Include a screen capture of your null distribution in your report.

(t) How well does the mathematical model/-distribution predict the behavior of the *t*-statistics?

(u) Are these p-values much different from what we found before?

The Central Limit Theorem predicts that the behavior of the sample means will be approximately normal even when the population distribution is not normal, as long as the sample size is sufficiently large. This tells us that the actual shape of the population, unless it is severly skewed or has major outliers, is not very important. Be sure to check this condition before you blindly use a *t*-distribution though!