0.5):

for n, yielding the sample size

in the case of using 0.5 as the most conservative estimate of the proportion. (Note: W/2 = margin of error.)

Otherwise, the formula would be which yields

In the right-hand figure one can observe how sample sizes for binomial proportions change given different confidence levels and margins of error.

For example, in estimating the proportion of the U.S. population supporting a presidential candidate with a 95% confidence