[mturmon]

Yes, it is OK to stop at the end if you fix the number of tests in advance.

There are more general conditions than deciding in advance. The relevant theory in that case is the sequential likelihood ratio test (http://en.wikipedia.org/wiki/Sequential_probability_ratio_te...).

Typically, in an SLRT for a series of independent trials, you compute a running sum of likelihood terms (accumulating as you go) and then at some point you stop if the sum goes above one line or below another line. The separation between the lines tells you how much variability is "allowed" in the partial sums.