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.
The interval for a difference has the shape every interval in this course has: the observed difference, plus or minus a margin of error. For a new checkout system converting 138 of 300 shoppers against the old one's 90 of 250, that is 0.10 ± 1.96(0.0418), or about 1.8 to 18.2 percentage points. What makes it its own topic is a thing it refuses to do. The two-proportion test merges the samples into one pooled estimate, because its null hypothesis says the two rates are equal and under that assumption there is one rate to estimate. An interval assumes nothing — estimating the difference is its entire job — so combining the groups would build in the claim that the difference is zero, the very thing being measured. On this study the two standard errors differ by under one percent and the error hides. So this animation goes looking for a study where it does not: at 110 of 300 against 72 of 250, the correct interval excludes zero and the pooled one contains it. Same data, same level, opposite conclusions.