How can you tell if one birth rate is statistically significantly different from another

Let the two birthrates (children born to 1000 population) be X and Y.
Under Ho that the two samples are from the same population with proportion of children born P,
both X and Y are Binomial with parameters n=1000 and P.
X/1000 and Y/1000 are normally distributed with common mean P and common sd = sqrt (PQ/n).
X/1000 - Y/1000 is normal with mean 0 and sd = sqrt (2PQ/1000).
The Z test statistic is
Z = (X/1000 - Y/1000)/sqrt (2PQ/1000)
Here, unknown P is estimated and Q = 1-P.
Estimate of P is Phat = (x+y)/2000

Hope this helps.