In statistics , a sample should be random, have a sample size less than one-tenth of the population and be normally distributed for it to be viable for simple statistical analysis. I understand fully the random and normal parts, but why does having less than $1/10$th of the population make it independent? Why $1/10$th? Doesn't the sample get more accurate if it has more of the population in it? This rule just seems a bit counter-intuitive and I was wondering if anyone had a good explanation of its reasons.
2026-03-29 12:38:41.1774787921
Statistics Sample requirements
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Your question probably is in the context of Bernoulli Trials (which by definition must be independent). If you're sampling from a finite population that assumption is violated because you are sampling without replacement (so the trials wouldn't be independent). The rule of thumb is if the sample is less than $10\%$ of the population then it's still okay to proceed with the statistical analysis. The issue here isn't about accuracy but whether or not the trials are independent. If you are sampling from a larger subset of the overarching population then you increase the probability of picking the same observation twice; hence you are more likely to violate the assumption that the trials are independent. That being said $10\%$ isn't some magic number, its just a heuristic.