The first is using the normal approximation to the binaomial where means and

variances are matched between the binomial and the normal approximation.

This is assuming that np and nq are large.

The lower formula looks to use a better approximation, and so have a wider

range of validity.

Now I would expect that the lower formula might be used in software packages,

but for hand calculation I would use the upper formula unless

np and or nq are small, then I suspect I would use the bootstrap or the

exact binomial calculations.

RonL