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

Under Neyman allocation, sample sizes are proportional to the arm standard deviations. HereFor total size $n_{\max }$, the minimized asymptotic variance isEqual allocation givesThe Neyman allocation therefore reduces the large-sample variance by $0.04/n_{\max }$, about $5.9\%$ of the equal-allocation variance.