&gt;  I don&#x27;t disagree with the math, but wouldn&#x27;t it be the case that it&#x27;s easier to get a biased sample from 1000&#x2F;100M people than 1000&#x2F;1M people?<p>It&#x27;s not the population size that matters; it&#x27;s the variance in the underlying population.<p>Mathematically, the sample size needed to construct an n% confidence interval for a normal distribution is independent of the population size (the first derivative is zero).