With equal allocation and true alternative rates $\lambda_T,\lambda_C$, the asymptotic variance is
$$
V_A=\frac2N\left(\frac1{\lambda_T}+\frac1{\lambda_C}\right).
$$
The normal approximation requires $|\log RR_A|/\sqrt{V_A}\geq z_{1-\alpha/2}+z_{1-\beta}$. Hence
$$
N=\frac{2(z_{1-\alpha/2}+z_{1-\beta})^2}
{(\log RR_A)^2}
\left(\frac1{\lambda_T}+\frac1{\lambda_C}\right),
$$
rounded upward. Writing $\lambda_T=RR_A\lambda_C$ expresses it using a specified control rate and the target rate ratio.


Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-207/3/e/solution