Question

Suppose a random sample of size 55 is selected from a population with σ = 9....

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.

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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