(See below for two answers about the math that gets to 5%.) > We want a margin of error of 1 percentage point (kinda reasonable, since their estimate is stated

(See below for two answers about the math that gets to 5%.) > We want a margin of error of 1 percentage point (kinda reasonable, since their estimate is stated as a percentage without explicitly stating the margin of error) If the question they want to answer is "give me the exact % of bots on Twitter", then yes, you probably want a standard deviation of less than 1%. That would take many thousands of samples, as you say - much larger than sample sizes used in presidential elections, even. OTOH, my guess is that the question for them is "are bots a big part of the Twitter population?" In that case, 97% of accounts being real versus 96% doesn't matter much, since both show bots are a very small group. (But maybe bots write a disproportionately large # of tweets?)