StatisticsdrillA/B test: confidence interval for the difference
A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.
The task
An A/B test of a checkout page: control, 120 conversions out of 1,000 visitors; variant, 135 out of 1,000. Build a 95% confidence interval for the difference in conversion rates, pB - pA (variant minus control), using the unpooled standard error √( p̂A(1 - p̂A)/nA + p̂B(1 - p̂B)/nB ). Use z* = 1.96. What is the upper limit? Give it as a proportion (0.0123 means 1.23 percentage points). Round to 4 decimal places.
What this problem teaches
The test of pA = pB pools the two rates because it assumes they are equal under H0. The interval does not assume that, so it uses each group's own rate in the standard error. An interval that includes 0 means the lift is not established.
A hint if you get stuck
(p̂B - p̂A) ± z* × SE, with SE built from each group's own rate. The upper limit adds the margin.
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