Determine which of the following four population size and sample size combinations would not require the use of the finite population correction factor in calculating the standard error.
A. N = 15,000; n = 1,000
B. N = 150; n = 25
C. N = 2500; n = 75
D. N = 1500; n = 300
To determine which of the four combinations would not require the use of the finite population correction factor in calculating the standard error, we need to compare the sample size (n) to the population size (N).
The finite population correction factor is used when the sample size is a significant portion of the population size. When the sample size is small relative to the population size, the correction factor is not necessary.
In general, if the sample size is less than 5% of the population size (n < 0.05*N), the correction factor is not needed.
So, let's check each combination:
A. N = 15,000; n = 1,000
Here, n is 6.67% (1000/15000) of N, which is greater than the 5% threshold. Therefore, the finite population correction factor would be required.
B. N = 150; n = 25
In this case, n is 16.67% (25/150) of N, which is greater than the 5% threshold. So, the finite population correction factor would be needed.
C. N = 2500; n = 75
Here, n is 3% (75/2500) of N, which is less than the 5% threshold. Hence, the finite population correction factor is not required.
D. N = 1500; n = 300
In this combination, n is 20% (300/1500) of N, which is greater than the 5% threshold. Therefore, the finite population correction factor would be needed.
So, based on the calculations, the combination that does not require the use of the finite population correction factor is:
C. N = 2500; n = 75.