Question

Suppose a random sample of size 49 is selected from a population with standard deviation = 8. 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

For finite population the finite correction factor is as

Where n = sample size and N = population size.

a) Here population is infinite so that n/N tend to zero.

So standard error of sample mean is as

b) Here N = 50000

So standard error of sample mean is as

c)

Here N = 5000

So standard error of sample mean is as

d) Here N = 500

So standard error of sample mean is as