Question

Suppose a random sample of size 59 is selected from a population with σ = 10. 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).

Answer 1

Solution :

Given that ,

standard deviation = = 10

a) n = 59

= / n = 10/ 59 = 1.30

b) N = 50000

=  N - n / N - 1 * / n

=   50000 - 59 / 50000 - 1 * 10/ 59 = 1.30

c) N = 5000

=  N - n / N - 1 * / n

=   5000 - 59 / 5000 - 1 * 10/ 59 = 1.29

d) N = 500

=  N - n / N - 1 * / n

=   500 - 59 / 500 - 1 * 10/ 59 = 1.22