Answer to Question #39961 in Statistics and Probability for Precht

Question

I realise that my question is quite simplistic for this site but I will ask anyway. I am wondering if Percentage results become more unreliable the smaller the group is(I am not referring to a sample of the group rather questioning the whole group). If yes, is there a way to determine that? For example 5% of the 30 people that received a direct-sales call hang up the phone = Does that mean that 30% of 8 people called would be expected to hang up? or is the percentage unreliable the smaller the number which is my main question? I hope that this was clear enough. Thank you very much

Answer 1

Your thought that the reliability of p^ is reduced for small p is correct. Consider the case of a sample of a single person. You can build a Binomial confidence interval around p^ - it's determined only by the number of 'successes' and the number of total events (n). This confidence interval will reflect the uncertainty caused by the finite size of the sample - the smaller n is, the larger the interval will become.