Question

Suppose a random sample of size 56 is selected from a population with  = 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).

The population size is infinite (to 2 decimals).

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

The population size is N = 5,000 (to 2 decimals).

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

Answer 1

The population standard deviation is . A sample of size n=56 is selected.

• When the population size is infinite, the standard error of the mean is calculated as

The population size is considered finite if the sample size is greater than 5% of the population. That is if N is the size of the population, then we need to apply finite population correction factor, when the sample size n is

When the population size is finite, the standard error of the mean is calculated as

.

• The population size is N = 50,000.

The sample size is 56. n/N = 56/50000=0.0011. This value is not greater than 0.05. Hence we will not use the finite population correction factor.

When the population size is N = 50,000 the standard error of mean for a sample of size n=56, remains

• The population size is N = 5,000

The sample size is 56. n/N = 56/5000=0.011. This value is not greater than 0.05. Hence we will not use the finite population correction factor.

When the population size is N = 5,000 the standard error of mean for a sample of size n=56, remains

• The population size is N = 500

The sample size is 56. n/N = 56/500=0.11. This value is greater than 0.05. Hence we will use the finite population correction factor.

When the population size is N = 500 the standard error of mean for a sample of size n=56, is