Reason for returning sample to population when polling n samples
In a tutorial on sampling distribution, it gave an example of predicting customer satisfiability by questioning a sample of the whole population (where the population refers to all of the customers). It was stated that you get the sampling distribution of a statistic "by computing the statistic for all possible samples of a specific size drawn from the same population". The example given was taking 100 users from the entire population, questioning them, returning the 100 people to the population, taking 100 more and then questioning them, and doing this n number of times.
Why do we return the 100 people already questioned back to the population instead of getting the next 100 people from what's left? Even though the probability might not be very large, you could still end up with a situation where you're asking a large number of the same people multiple times.
Re: Reason for returning sample to population when polling n samples
Lets take a simplified case were the population small so its practical to compute the exact sampling distribution.
Population size 3 people (A,B,C)
Suppose your sample size will be 2.
There are 3 possible samples: AB,AC,BC.
Lets say we followed your method and randomly sampled (AB), but did not return them to the population. What will happen next? there is only 1 person left for you to sample from but you cant include A or B in any future sample; so your calculation will ignore any results associated with AC and BC.