Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 207 / 3 / d / Solution

Let $\pi$ be the new-treatment response probability in the trial's target population and let the fixed historical standard-of-care rate be ${\pi }_0$. The one-sided hypotheses areThe boundary $\pi ={\pi }_0$ determines the type-I error because rejection probability increases with $\pi$.