Use the expression in the accompanying discussion of sample size to find the size of each sample if you want to estimate the difference between proportions of men and women who own smartphones. Assume that you want 90â% confidence that your error is no more than 0.02. The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - α can be found by using the following expression:
E = zα/2âp1q1/n1 + p2q2/n2
Replace n1 and n2 by n in the preceding formula (assuming that both samples have the same size) and replace each of p1, q1, p2, and q2 by 0.5 (because their values are not known). Solving for n results in this expression:
n = Z2α/2/2E^2