True or false. To have a binomial setting, the following must be true: When sampling, the population must be at least 20 times as large as the sample size. (Some textbooks say 10 times as large.)

Question

I originally believed the answer was false. I thought sampling could be done with replacement. So, the condition, which is only necessary for when the trails are not independent, is not a must to have a binomial setting. However, I'm still unclear about this question. I would like your clarification.

Answer 1

When sampling without replacement, the size of the sample needs to be less than 10% of the population - the population is at least 10 times as large as the sample.