Here's the basic problem:

There are 19711 male births out of 38562 in coutry A
There are 17703 male births out of 35042 in cuntry B

Call the probability of a male birth p. Use the generalised likelihood ratio test to test the hypothesis that p has the same value in each country versus a suitable alternative.

Now I thought the generalised lkelihood ratio test was only used to test a null hypothesis based on just one distribution and don't know how we could use it to compare two samples, so how do we begin here?

Also, for country A, if we wanted to us the likelihood ratio statistic to test the hypothesis p = 0.5 against p not equal to 0.5, then I got a likelihood ratio statistic of 9.18. I haven't done any of these questions before, so if someone could just confirm this result that would be very helpful (just a simple "yes, that's right" would be fine!)