Defining the size of the random sample based upon expected proportional values

Question: How large should a sample be if I want the actual proportional value for the base population to be in a specific range around the measured proportional value of the sample?

Essential factors for this calculation are:

1. The expected proportional value

If the proportional value cannot be predicted, a worst-case scenario is assumed, i.e. an expected proportional value of 50%.

2. The tolerated difference of the proportional values

i.e. the maximum extent to which the actual value of the population may deviate from the measured value of the sample

3. The desired significance level

i.e. the statistical probability that the actual proportional value of the population is within the tolerated range of variation around the measured proportional value of the sample – in market research, we normally target a significance level of 95%.