Math Help - [SOLVED] population proportion

1. [SOLVED] population proportion

2 populations are independently surveyed using s.r.s of size n, and 2 proportions, p1 and p2, are estimated. It is expected that both population proportions are close to 0.5. What should the sample size be so that the standard error of the difference, $\hat p_1-\hat p_2$ will be less than 0.02?

I can find $\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}(\frac{N-n}{N-1})}$ for the individual component, but I don't know how to apply for $\hat p_1-\hat p_2$.

2. I would set

$\sigma_{\hat p_1-\hat p_2}=\sqrt{ {p_1(1-p_1)\over n_1 }+{p_2(1-p_2)\over n_2 } }\le .02$

Then let all the p's equal .5 and $n_1=n_2=n$

$\biggl({1\over .02}\biggr)^2\le 2n$
So $n_1\ge 1250$ and $n_2\ge 1250$