Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 207 / 2 / a / i / Solution

PutAt a fixed alternative $\theta$, the approximate power of the Wald test increases as its variancedecreases. For fixed total sample size $n=n_0+n_1$, the allocation problem is thereforewith integer rounding applied after solving the continuous problem. The second-order condition is positivity of the second derivative at the stationary point.