What influences the sample size? we examine the effect of different inputs on determining the sample size needed to obtain a specific margin of error when finding a confidence interval for a proportion. find the sample size needed to give, with 95% confidence, a margin of error within plus-or-minus 6% when estimating a proportion. first, find the sample size needed if we have no prior knowledge about the population proportion p. then find the sample size needed if we have reason to believe that p almost-equals 0.7. finally, find the sample size needed if we assume p almost-equals 0.8.