I’ve seen two formulas for estimating a sample size proportion, the first one:
s = 1.96^2 * p * (1-p) / MOE^2
1.96is the Z score for getting a 95% confidence interval.
pis the estimated proportion (0.5 if unknown)
MOEis the margin of error (0.05)
This formula is independent from the total population. There’s also another one that reads:
S = N * s / (N + s - 1)
Nis the population.
sis the sample size estimated with the previous formula.
My question is, which of these would you use and when? (the second one seems more complete since it takes into account the population size).