Module 04 Activity

Scenario

Quantify how much you actually know, using simulation where the formula is unclear.

What you build

A numpy simulation study and a set of intervals whose interpretation you can defend.

Steps

1. Build a population, draw repeated samples, and look at the spread of the estimates. Confirm no single sample was wrong.
2. Repeat at three sample sizes and check the spread falls with the square root of n.
3. Compute the standard error from one sample with ddof=1 and compare it with the simulated spread of many.
4. Bootstrap a statistic with no simple formula, resampling with replace=True at the original size, at least a few thousand times.
5. Build intervals for a mean and for a proportion, using Wilson for the proportion, and tabulate width against n.
6. Write the interpretation of one interval in a sentence that would survive review, and list two wordings you rejected.

Evidence to hand in

• The sampling-variation simulation.
• The spread at three sample sizes against the square-root prediction.
• The standard error computed both ways, with the gap explained.
• The bootstrap distribution and its percentile interval.
• The width-against-n table.
• Your interpretation sentence and the rejected wordings.

Review checklist

• Every random step uses a seeded default_rng.
• ddof=1 is used for every sample standard deviation.
• The bootstrap resamples with replacement at the original sample size.
• Proportion intervals use Wilson rather than the normal approximation.
• The interpretation does not attribute probability to a computed interval.

Mark complete