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 two populations rather than the two samples, why the null's claim of equality is what lets you merge both samples into one estimate, why the test's standard error is not the interval's, and the design question that decides whether any of it applies.
Two checkout systems, two groups of shoppers, and a gap of ten points between them. That gap is a measured fact about 550 people; whether it says anything about the two systems is the question the test exists to answer. This animation writes the claim about the populations, strikes out the version written about the samples, and then does what the null's one sentence tells it to: if both populations share a single completion rate, estimate that one rate from all 550 shoppers at once. You will see why that pooled 228 of 550 is not the average of 0.46 and 0.36, why the test's standard error is not the interval's, and why one question about the design outranks all of the arithmetic. Twelve short steps; press Next for each one.