I don't know a lot about sampling methods.
I have a large population of size 2,000,000. I used one of those sample size calculators. It says that I need sample size of approximately 10,000.
I am trying to find the probability p of success for the population. It is not feasible for me to test all 2,000,000 members of the population. That is why I am sampling.
I assume that the sample size calculator means a simple random sample without replacement. I have read that a simple random sample with replacement ensures that the covariance between two variables is 0
, i.e., independent.
When should one choose with replacement instead of without replacement?
If we sample with replacement, then we are simply performing Bernoulli trials. I suppose this makes applying statistical tools (which?) easier.
Again, sampling ignoramus here.