A payment-accuracy team launched a rule intended to reduce incorrect payments. In a prior period (control), 10,000 transactions yielded 9,520 correct and 480 incorrect. In the post-launch period (treatment), 10,000 transactions yielded 9,640 correct and 360 incorrect. 1) Choose an appropriate hypothesis test and state H0 and H1 formally. 2) Compute the test statistic and two-sided p-value for the difference in accuracy (proportions). Show the pooled vs unpooled choices and justify which you use. 3) Construct a 95% confidence interval for the difference in proportions (treatment − control). 4) Interpret the results for a non-technical stakeholder in one sentence, including practical significance. 5) 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 you use and the numeric inputs (Z-scores).