Find how large n must be before a skewed population behaves
Three steps, the way the exam actually works: work through the lab, write down your own observations, then answer a 10-point free response. What you recorded goes to the grader with your writing, so a conclusion that does not follow from your own evidence will cost you the point — exactly as it would with a real reader.
Predict before you look
- The Central Limit Theorem says the sampling distribution of x̄ approaches Normal as n grows. Write down, before you begin, whether it says anything about how FAST.
- The common guideline is n ≥ 30. State in one line whether you expect that threshold to work equally well for a symmetric and a strongly skewed population.
Nothing to submit here — these are to think through, so the prediction below is an informed one rather than a guess.
Commit to an answer now. It is not graded and being wrong costs nothing — the point is to have something specific to reconcile against once you have the data.
Answer every prediction to unlock the lab. A sentence is enough.
Run the investigation
Predictions first
The procedure and the simulation unlock once you have committed above. Observing before predicting is how a wrong intuition survives a lab intact.
Record what you found
This is your reading of the source, not ours. The grader sees them, so your conclusions have to follow from what you actually recorded.
| σ reported for the Skewed right population | |
|---|---|
| μ reported for the Skewed right population | |
| Predicted SE, Skewed, n = 2 | |
| Predicted SE, Skewed, n = 25 | |
| Shape of the histogram of means, Normal population, n = 2 | |
| Shape of the histogram of means, Skewed population, n = 2 | |
| Smallest n tested at which the Skewed population's means look symmetric | |
| Shape of the histogram of means, Skewed population, n = 25 |
Answer the free response
Using your observations: (a) Compare the shape of the histogram of sample means at n = 2 for the two populations, and explain why they differ. (b) Describe how the Skewed population's histogram of means changed as n increased, and state the smallest n you tested at which it looked approximately symmetric. (c) Explain what your results show about the "n ≥ 30" guideline — specifically, whether it is a theorem, a safe universal threshold, or something else. (d) Explain why the population histogram itself never became more symmetric no matter how large you set n.
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