A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means irrespective of the size of the sample. whenever the sample size is more than \( 5 \% \) of the population size. whenever the sample size is less than \( 5 \% \) of the population is infinite.

When dealing with finite populations, the finite population correction factor (FPC) becomes important primarily when the sample size is a significant portion of the population. Generally, if your sample size exceeds 5% of the total population, it indicates that the selected sample may influence the overall characteristics of the population. So, using the FPC helps to adjust the standard deviation of the sample mean accordingly, ensuring more accurate estimates. In practical terms, consider a scenario where you are surveying a town with 1,000 residents, and you decide to pull a sample of 200. Since this sample constitutes 20% of the total populace, neglecting the FPC could lead to misleadingly precise standard error estimates. By applying the correction, your results will reflect a more realistic representation of the variability present in the whole population, making your findings more reliable and applicable.