Determine the confidence interval. This is how close the result of the study should be to the actual percentage. For example, in a poll that shows that 55 percent of people, plus or minus 2 percent, support the incumbent president, the confidence interval is 2 percent, which means that the actual percentage (because the poll is estimating based on the people it surveyed, not everyone in the area) is within 2 percentage points above or below the reported number, so it could be between 53 and 57.
Determine the confidence level. This is expressed as a Z-score, which is how many standard deviations away from the center the study needs to include. A confidence level of 95 percent would be a Z-score of 1.96 and would mean that there is a 95 percent chance that the true proportion lies within 1.96 standard deviations on either side of the mean.
Calculate the estimated proportions. For example, if 60 percent of people are expected to approve, use 0.6 for p.
Plug the numbers into the following formula and calculate the answer:
Sample size equals confidence level squared times p times the quantity of 1 minus p divided by the confidence interval squared
SS = (Z^2 * P * (1 - P))/C^2
For example, if you wanted to be 95 percent confident, expected the proportion to be 60 percent, and needed the estimate to be within 5 percentage points either way, you would use 1.96 for Z, 0.6 for P, and 0.05 for C, which would reveal the need for 369 people in the survey.