Suppose a random sample of size 40 is selected from a population with = 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).

Question

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

Some notes on finite population correction factor:

If the population is small and the sample is large (more than 5% of the small population), use the finite population correction factor.

For standard error of the mean, use:
sd/√n

If you need to adjust for the finite population correction factor, use:
sd/√n * √(N-n)/N-1)
N = number in population
n = number in sample

Therefore:

a. Use the formula sd/√n (population is infinite)

b. Is the sample size of 40 more than 5% of the population? No, it isn't; your answer will be the same as part a).

c. Is the sample size of 40 more than 5% of the population? No, it isn't; your answer will be the same as part a) and b).

d. Is the sample size of 40 more than 5% of the population? Yes, it is, so use the finite population correction factor.

I hope this will help get you started.