#StackBounty: #sampling #sample-size #proportion Which of these 2 formulas is the right one for estimating sample size for proportions?

Bounty: 50

I’ve seen two formulas for estimating a sample size proportion, the first one:

s = 1.96^2 * p * (1-p) / MOE^2


  • 1.96 is the Z score for getting a 95% confidence interval.
  • p is the estimated proportion (0.5 if unknown)
  • MOE is 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)


  • N is the population.
  • s is 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).

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