The assignment for this response was to discuss “…under what circumstances the Finite Population Correction Factor (FPCF) is necessary and why is it necessary? How does the adjusted z-value vary quantitatively (bigger, smaller, much larger, no change) from the normal value?” This was the first written response for my Statistics II class (actually called “Quantitative Tools for Management” in the course catalog, but it is roughly equivalent to a Stats II course) during the current semester (Spring 2007) at the University of Massachusetts at Amherst’s online program; I earned a 5/5 for my response below:
When a sample is greater than 5% of the population from which it is being selected and the sample is chosen without replacement, the finite population correction factor should be used. The adjusted z-value would be larger than the normal z-value, meaning that the value is more standard deviations from the middle than in a non-adjusted z-value.
This factor adjusts the z-value to show the extra precision obtained from the sample size being a greater fraction of the population size than normal. Since the standard deviation becomes smaller as the sample size increases, the FPCF shows that a value in a large sample size not at or near the mean is a greater number of standards deviations from the mean than in a small sample size. In other words it’s rarer for a value in a large sample size to be far away from the mean compared to a small sample size.