Solution

It is a factor that is used to correct the standard error of a sample mean where the sample is obtained without replacement and the sample size is as a minimum of 5% of the total population. The value of finite population correction factor is always less than one. The need for finite population correction factor arises because the central limit theorem does not hold under these conditions and the standard error of the estimates is large. In essential terms, it draws the distinction between sampling without and with replacement. When a sample size is more than 5% of the population, the finite population correction factor defines both the standard error of the mean as well as the standard error of the proportion. The formula for the finite population correction factor is defined as follows: