Defining the size of random samples due to expected proportional value differences

Question: How large should my (sub) samples be if I want a difference of proportional values between two samples to be significant?

Crucial factors for this calculation are:

1. The expected proportional values

If it is not possible to approximately predict the proportional values, a worst-case scenario is assumed for the calculation, i.e. expected proportional values of 50%.

2. The desired significance level

i.e. the statistical probability that two proportional values actually differ from one another. Market research normally targets a significance level of 95%.