Confidence level for Binomial

Question

For 617519 first time births there were 317528 boys. Give an estimate with 99% confidence interval for the probability that the first time birth is a boy.

I have searched for the confidence interval function. However, I cannot find any match with probability and confidence interval within the HypothesisTesting package.

The result I am looking for is:

(*0.51255,0.51583*)

Answer 1

The ratio is the estimate of the p parameter for presumed binomial distribution. The central limit theorem justifies use of the normal approximation for calculation of interval.

n = 617519;
m = 317528;
p = m/n;
z = Quantile[NormalDistribution[], {0.005, 0.995}]
ci =p + # Sqrt[(1/n) p (1 - p)] & /@ z

yielding:

{0.512561, 0.515838}