 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-207/3/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The pooled Wald test statistic is

T = \frac{p _{1} - p _{0}}{p ˉ ( 1 - p ˉ ) ( 1/ n _{1} + 1/ n _{0} )} .

In asymptotic calculations one replaces

\overset{p}{ˉ}

by its probability limit

\overset{π}{ˉ} = (n_{1} π_{1} + n_{0} π_{0}) / (n_{1} + n_{0})

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