Solution (source code)

= Solution
{c}

The observed statistic $94.34$ exceeds the supplied $0.999$ quantile $13.82$ for two degrees of freedom. Thus \b[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 \b[the data support the proposed association]: mixed-sex first pairs are associated with a greater tendency to stop at two children.