Mistake Master
A Large p-Value Fails to Convict. It Does Not Acquit
You'll learnhow to carry a two-proportion z-test from statistic to sentence — the gap divided by the pooled standard error, the p-value as a tail area of the null's own distribution, a conclusion that carries the direction and both populations, why failing to reject never becomes a finding of equality, and how the test lines up with the interval built from the same data.
The arithmetic left after Topic 3.12's setup is one division and one area. The observed gap of 0.10 sits 2.37 pooled standard errors from where the null expects it, and two populations with a shared rate would produce a gap that far out about nine times in a thousand. Every beat here is drawn on the null's own sampling distribution — the world the null describes, drawn as a curve — with the observed gap planted on it and the p-value shaded in. Then comes the sentence, which is where this topic is actually lost: a small p-value earns a direction and two populations, a large one earns precisely "not convincing evidence", and a pilot study with a p-value of 0.28 has not shown two systems equal, because at its sample sizes only a gap past eleven points was ever going to register. Twelve short steps; press Next for each one.