Question

What is a Finite Population Correction Factor?

Please explain its concept in detail

Answer 1

in sampling without replacement for finite population we have

Standard deviation of our x bar = (S.D/ root(n))  , where n is the sample size and x bar is your sample mean

to understand the concept finite population correction factor first we need to understand what sampling fraction(f) is

f= n/N , N is your population size

if this proportion(f) > 0.05 we say that sample size is significant with respect to your population size and hence we cannot assume  f~0 ,

now if n is significant with respect to your N , the standard deviation of your estimate in our case mean will be large to control this we introduce one more term to control this we call finite population correction factor

FPC= root (1-f)

we multiply this factor with our S.D of estimate

S.D of mean(xbar)= (S.D/ root(n)) * root(1-f)

range of f= 0<f<=1

thankyou!