Question

Why is sampling without replacement acceptable with a large population?

Answer 1

When sampling without replacement, the results of sampling after taking the first sample are dependent on the results of the preceding sampling. However if the sample size is very small compared with the size of the population, this dependence is usually insignificant.

Answer 2

Answer:

In sampling without replacement, each sample unit of the population has only one chance to be selected in the sample.

The sampling without replacement is acceptable with a large population because, when the sample size is very large, removing one sample doesn't impact the overall distribution. Replacement has very little effect on the probabilities.

Like we have a sample of 1000 things and 1 is removed, so that will not affect the overall sample much.