Past exam of the probability, statistics and options I course of the University of Oxford / 2010 / O / 3 / c / Solution

The observed statistic $94.34$ exceeds the supplied $0.999$ quantile $13.82$ for two degrees of freedom. Thus reject independence, with $p<0.001$.

For one child of each sex among the first two, the three-child count is $3393$, below its independence expectation $3763.1$. Equivalently, the two-child count is $13079$, above its expectation $16472-3763.1=12708.9$. These departures have exactly the direction predicted by the suggestion. Thus the data support the proposed association: mixed-sex first pairs are associated with a greater tendency to stop at two children.