Show that sample size buys precision and never accuracy
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
- An estimator is unbiased if its sampling distribution is centered at the parameter. State whether you expect that centering to depend on the sample size.
- Distinguish, in one line each, what "precise" and "accurate" mean for an estimate. They are not synonyms.
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.
| μ reported for the Bimodal population | |
|---|---|
| σ reported for the Bimodal population | |
| Predicted SE, Bimodal, n = 5 | |
| Predicted SE, Bimodal, n = 25 | |
| Predicted SE, Bimodal, n = 50 | |
| Mean of the sample means at n = 5 | |
| Mean of the sample means at n = 25 | |
| Did the population histogram change as n rose? |
Answer the free response
Using your recorded values: (a) Compare the mean of the sample means at n = 5 and at n = 25 with the population μ, and state what property of x̄ this demonstrates. (b) Compare the predicted standard errors at n = 5, 25 and 50 and describe the trend. (c) Using (a) and (b) together, explain the difference between precision and accuracy, and state which one sample size controls. (d) A researcher using a biased sampling method proposes to fix the problem by collecting ten times as much data. Evaluate that proposal using what this investigation showed.
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