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In different situations there are many tests or general agreements for a minimum sample size, which are usually some fixed number that is not that high, capping at <400. Common numbers include 100, 30, etc. But wouldn't minimum sample size based on proportion make more sense? Say if you sample 100 bacteria out of a population of 1 billion. That does not seem like a very representative sample.

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    $\begingroup$ The aim with random sampling is not to guarantee "representativeness" within each sample. The point is to get some level of accuracy/precision of some quantity (on probabilistic grounds), and those calculations are pretty insensitive to population size. $\endgroup$ – Glen_b Oct 5 at 3:55
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    $\begingroup$ Imagine you are taking a sample, and you are calculating the mean of that sample. If you do that many times, you get a distribution of sample means. That distribution will have a variance, and this variance depends on the number in each sample, not on the number in the population. $\endgroup$ – Old_Mortality Oct 5 at 4:22

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