Determine the size of the population you wish to survey an opinion. For example, the United States contains a population of about 300 million people.
Assume the parameters that you wish to employ. For this example, we will assume a 95 percent confidence, a margin of error of 5 percent, and a historical proportion of survey respondents with a similar view of 50 percent. This historical proportion is the default when it is unknown.
Calculate alpha, and the critical standard score (z). Alpha is computed by one minus the confidence interval or 1 - .95 = .05. The critical score is determined by first taking the equation 1 - alpha/2 or 1 - .025 = .975 and then plugging that number into a Normal Calculator which results in a value of 1.96. Normal Calculators can be found online and a mean value of 0 and standard deviation value of 1 must be used for this result.
Examine the formula for sample size and plug in the numbers from the values found and assumed above. The formula is as follows:
Sample Size = ((z^2 X p X q) + ME^2) / (ME^2)
Where z is the z score, p is the historical proportion, q is (1 - p) and the ME is the margin of error and N is the total population.
Plug in the numbers for the equation and compute the result.
Sample size = ((1.96^2 X .5 X .5) + .05^2)/.05^2
Sample size = 385