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Just a note
An empirical way to estimate how the size of population sampled affects how your results vary, is to repeatedly take samples from our farmer's experimental population of 5 observations (a) with replacement and (b) without replacement  and compare the variance of their sample means. (a) The variance of 5000 means of 3 observations, taken with replacement, was 78.8 (b) The variance of 5000 means of 3 observations, taken without replacement, was only 39.1
