Mistake Master
An Interval Assumes Nothing, Which Is Exactly Why It May Not Pool
You'll learnto build a two-proportion z-interval from each group's own estimate, why pooling belongs to the test and never to the interval — shown on a study where it changes the conclusion — how the confidence level trades width for certainty, and how to write an interpretation that names both populations and the direction of subtraction.
A store's new checkout system finishes 138 of 300 customers and the old one 90 of 250, a difference of 10 percentage points. A confidence interval puts a range around that estimate: 0.10 give or take 0.082, so (0.018, 0.182) at the 95% level. Two things about it are worth more than the arithmetic. The first is that the standard error keeps the two groups apart, because an interval assumes nothing about whether the rates are equal — and pooling, which the test does, is not merely wrong in principle. This page searches the study design for a case where it changes the answer, finds one at 110 of 300 against 72 of 250, and draws the two intervals straddling zero from opposite sides. The second is that the confidence level is a lever: the same data give an interval that excludes zero at 95% and includes it at 99%. Twelve short steps; press Next for each one.