Test payment-accuracy lift with p-value and power

Q: Test payment-accuracy lift with p-value and power

This question evaluates proficiency in hypothesis testing for proportions, interpretation of p-values and confidence intervals, and power/sample-size calculations within the Statistics & Math domain for a Data Scientist role.

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Question

AB Test of Payment Accuracy (Two Proportions)

Assume transactions in the two periods are independent and large enough for normal approximations. Define "success" as a correct payment (accuracy).

Control (pre-launch): n = 10,000, correct = 9,520, incorrect = 480
Treatment (post-launch): n = 10,000, correct = 9,640, incorrect = 360

Tasks

Choose an appropriate hypothesis test and state H0 and H1 formally.
Compute the test statistic and two-sided p-value for the difference in accuracy (proportions). Show pooled vs unpooled standard error choices and justify which you use for the test.
Construct a 95% confidence interval (CI) for the difference in proportions (treatment − control).
Interpret the results for a non-technical stakeholder in one sentence, including practical significance.
Power planning: If baseline accuracy is 96.0%, what equal per-group sample size is needed to detect an absolute improvement of 0.2 percentage points (to 96.2%) with 80% power at α = 0.05 (two-sided), using the normal approximation? Show the formula and numeric inputs (Z-scores).

Test payment-accuracy lift with p-value and power

AB Test of Payment Accuracy (Two Proportions)

Solution

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Test payment-accuracy lift with p-value and power

Overview

AB Test of Payment Accuracy (Two Proportions)

Solution

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