It’s tricky. I at first thought that he was talking about sampling families, but he isn’t.
The expected fraction G/(G+B) over many trials, where each trial t involves N families and leads to Gt girls and Bt boys, is not (sum of Gt) / (sum of (Gt + Bt)).
Trials that result in a smaller number of children have more boys than girls. Trials that result in an unusually large number of children have more girls than boys. Yet both kinds of trials count as 1 sample when computing the average fraction of girls. So the average population fraction is smaller than the population fraction from all those trials.
It’s tricky. I at first thought that he was talking about sampling families, but he isn’t.
The expected fraction G/(G+B) over many trials, where each trial t involves N families and leads to Gt girls and Bt boys, is not (sum of Gt) / (sum of (Gt + Bt)).
Trials that result in a smaller number of children have more boys than girls. Trials that result in an unusually large number of children have more girls than boys. Yet both kinds of trials count as 1 sample when computing the average fraction of girls. So the average population fraction is smaller than the population fraction from all those trials.