Question

Suppose a random sample of size 55 is selected from a population
with σ = 9. Find the value of the standard error of the mean in
each of the following cases (use the finite population correction
factor if appropriate).

**a.** The population size is infinite (to 2
decimals).

**b.** The population size is *N* = 50,000
(to 2 decimals).

**c.** The population size is *N* = 5000 (to
2 decimals).

**d.** The population size is *N* = 500 (to
2 decimals).

Please show excel formula or functions if this can be solved in excel. Thanks.

Answer #1

Ans:

when sample size is less than 5% of the population size,we do not use finite population correction factor.

a)population is infinite

standard error of mean=9/sqrt(55)=**1.21**

b)sample size is 0.1% of population size

standard error of mean=9/sqrt(55)=**1.21**

c)sample size is 1.1% of population size

standard error of mean=9/sqrt(55)=**1.21**

d)sample size is 11% of population size,so we will use FPC

FPC=sqrt((500-55)/(500-1))=0.9443

standard error of
mean=0.9443*9/sqrt(55)=**1.15**

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