Mistake Master
The Null Says One Proportion, So the Test Estimates One Proportion
You'll learnhow to set up a test for the difference between two population proportions: hypotheses written about the parameters rather than the samples, why the null's claim of equality is what licenses pooling both samples into one estimate, why the pooled standard error differs from the interval's, and the conditions — including the design question that decides whether the procedure applies at all.
A two-proportion test asks one question: could the gap between these two samples have come from two populations with the same proportion? Everything in the setup follows from that sentence. The hypotheses are about the two population proportions — never the sample values, which are known, unequal, and not up for testing. The null names no number, only equality, and that is not a gap in the setup but its engine: if the two populations share one proportion, then both samples are estimating the same thing, and the best estimate of it uses all 550 shoppers at once. That pooled estimate is a weighted average — 228 of 550, not the average of 0.46 and 0.36 — and it feeds a standard error that is deliberately not the interval's. Last comes a checklist with two of everything, and one question that outranks the arithmetic: are these two groups actually independent?