Have you taken into account the Covariance term while calculating the variance? The Covariance term becomes 0 when sampling is done With Replacement; but that will not vanish in case of Without Replacement.
I'm trying to show that the sample variance obtained from a random sampling without replacement is
and \mu is the sample mean. A lot of books cite the factor as a correction for small samples, but I couldn't derive it. Could someone help me here, please?
Thanks again, Sambit.
I saw this expression, but I don't know how to derive it. Most books only mention it but does not show how to obtain this formula. I was reading Kish's Survey Sampling book, but he just mention it as a correction for finite sample with replacement. I found some links from the University of Texas, but they also just mention the covariance without showing all calculations behind.
I'm stuck. I have no clue how to calculate this covariance. Could you give some hint, please?
This problem is driving me crazy!