Suppose a tv company wishes to estimate proportion of homes with at least 2 televisions. Suppose in fact unbeknown to the tv company the true population proportion is 0.70, while the proportion of homes which may be contacted by phone which have more than 2 tv's is 0.72.

Two possible surverys are being considered. Survey 1 is random sample of 200 from population of all homes. while survey 2 is a random sample of 400 homes taken from a register of homes with phones. The question is to find the mean square error for each of these methods of estimating the true proportion.

I tried to start this question, i'm thinking proportion with greater than 2 tv's in both surveys is binomial rv. So the next thing I do is maybe estimate the proportion using maximum likelihhod estimation and then do I find the Mse from that?