Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 41 / 2 / a / Solution

The two independent binomial distributions give fitted event probabilities $24/99$ and $12/100$. Their odds ratio and log odds ratio areUsing the log odds ratio variance from a two-by-two table,The stated normal approximation and quantile approximately two give the confidence intervalExponentiation gives the corresponding odds ratio interval $(1.0824,5.0876)$. Its lower endpoint exceeds one.