Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 2 / e / Solution

Under $H_0$, $(Z_1,Z_2)$ is a bivariate standard normal distribution with correlation $\rho =\sqrt{m_1/m_2}$. Rejection occurs either at stage 1 through $Z_1\ge u_1$, or at stage 2 through $Z_2\ge u_2$ after continuation $l_1<Z_1<u_1$. Hence the Type I error isThe final lack-of-benefit boundary $l_2$ affects acceptance, but not the probability of crossing an efficacy boundary.