Hey sazzy.

You can use what is known as a Wald test which uses the sample to get an estimate of the standard deviation which is commonly referred to as the standard error.

Given your estimate of p (call it p_hat), the estimate of the standard deviation is given by SQRT(p_hat*(1 - p_hat)/n) where n is the number of observations in your total sample.

You can derive this using the MLE estimator for p_hat and the invariance principle considering estimators of a function of an MLE estimate (in this case your function f is f(x) = x*(1-x) and x is your MLE estimate for your proportion parameter p).