Assuming 95% Confidence Level & 8% Margin of Error, a population frame of 37 yields a sample size of 30 (81% of pop) but a population frame of 370 yields a sample size of 107 (29% of pop) and a population frame of 3,700 yields a sample size of 144 (3.9% of pop).
As a layman, I would think that a larger population frame would require a larger proportion of the population to be representative. However, the required sample size tends towards an asymptote with larger population size.
Could anyone explain this phenomenon? Thank you!