Module 04 Activity

Scenario

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

What you build

A 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 that no single sample was wrong.
2. Repeat at three sample sizes and check that the spread falls with the square root of n.
3. Compute the standard error from one sample and verify it against the simulated spread of many.
4. Bootstrap a statistic that has no simple formula — a median, a ratio, a trimmed mean — with at least a few thousand resamples, seeded.
5. Build intervals for a mean and for a proportion, and tabulate how the width changes with 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.
• The bootstrap distribution and its percentile interval.
• The width-against-n table.
• Your interpretation sentence and the rejected wordings.

Review checklist

• Every random step is seeded.
• The simulated and formula standard errors agree.
• The bootstrap resamples with replacement at the original sample size.
• Every estimate is reported with an interval.
• The interpretation does not attribute probability to a computed interval.

Mark complete