Module 04 Summary

What this module established

Every sample from the same population gives a different answer. Five samples of 30 landed up to 24 away from a population mean of 500; across 1000 samples the spread was 18.22 and the extremes ran from 434 to 577.

Carry forward

• The distribution of the data and the distribution of the mean are different things. A strongly skewed population gave a symmetric, narrow sampling distribution at n = 200.
• SD describes values; SE describes the estimate and falls with the square root of n. The one-sample SE estimate is itself uncertain — it differed from the simulated value by 13%.
• The bootstrap gives an interval for statistics with no formula. Use replace=True, or every resample has the same mean.
• Use Wilson intervals for proportions; the textbook normal approximation misbehaves at small n and near 0 or 1.

Before moving on

Move on when you can explain why 'there is a 95% chance the true mean lies in this interval' is wrong, and say what is right instead.

Mark complete