Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 3 / a

Under the boundary null $p={\pi }_0=0.20$, rejection requires both $X_1>r_1$ and $X_1+X_2\ge r$. Independence of the two binomial distributions givesThe rejection event is increasing in $p$, so this boundary value is the supremum over the composite null $p\le {\pi }_0$.