To determine which population size and sample size combination would not require the use of the finite population correction factor, 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 large proportion of the population size (typically more than 5-10% of the population). It adjusts the standard error calculation to account for the finite population, ensuring more accurate estimates.
Let's examine each combination:
A. N = 1500; n = 300
In this case, n/N = 300/1500 = 0.2, which is less than 10%. The sample size is not a large proportion of the population size, so the finite population correction factor would not be required.
B. N = 2500; n = 75
Here, n/N = 75/2500 = 0.03, which is significantly less than 10%. The sample size is also not a large proportion of the population size, so the finite population correction factor would not be necessary.
C. N = 15,000; n = 1,000
In this combination, n/N = 1000/15000 = 0.0667, which is still less than 10%. Therefore, the finite population correction factor would not be required.
D. N = 150; n = 25
Here, n/N = 25/150 = 0.1667, which is greater than 10%. The sample size is a large proportion of the population size, so the finite population correction factor would be needed.
Based on the analysis, options A, B, and C (N = 1500; n = 300, N = 2500; n = 75, and N = 15000; n = 1000) would not require the use of the finite population correction factor. Option D (N = 150; n = 25) would require using the correction factor.
Therefore, the correct answer is A.