Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 46 / 2 / c / Solution

Define the difference as control minus intervention, positive for fewer deaths under intervention assignment. The observed difference per thousand isFor independent binomial distributions, its unpooled standard error per thousand isThe approximate 95% confidence interval is thereforeThe rare-event Poisson standard error $\sqrt{148+123}/30$ gives almost the same interval. A reduction of 1.5 per thousand is consistent with the data, since it lies inside the interval. Zero also lies inside, so a nonzero benefit is not established at the two-sided 5% significance level. This does not establish equivalence or prove the proposed effect size, and cannot by itself establish treatment contamination.