Finite Population Correction Factor Or Fpcf)

If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard error must be adjusted by multiplying it by the finite population correction factor as:

FPCF is described by   =

Whereas N = population size

                 n = sample size

Illustration

A manager wants an estimate of sales of salesmen in his company. A random sample 100 out of 500 salesmen is chosen and average sales are found to be Shs. 75,000. If a sample standard deviation is Shs. 15000 then determines the population mean at 99 percent level of confidence

Solution

Now N = 500, n = 100,  x¯ = 75000 and S = 15000

Here

Standard error of mean

S_{x¯ =} (s/√n) * {}

= (15,000/√100) * (√ {(500 - 100)/(500 - 1)})

= (15,000/10) * (0.895)

S_x¯ = 1342.50 at 99 percent level of confidence

Population mean         = x¯ ± 2.58 S_x¯

                                    =shs 75000 ± 2.58(1342.50)

                                    =shs 75000 ± 3464

                                    = Shs 71536 to 78464