for the most part, statistics assumes indefinitely large population and absolute sample size. For most testing purposes, even 100 would give you a suprisingly good confidence (e.g., imagine you want to reject that coin is at least 60 to 40 unfair, 100 tries is plenty to reject that with a good enough confidence).
The real question usually is not about a size of the sample, but about the sampling technique (i.e., is it truly random). That's by far the most common way to lie with statistics. I.e., to apply a test to a sample collected with a bias.