Sample Size Requirement is too big!

Someone asked me recently about sample size computations. Based on my experience this is one of the most difficult questions to answer because much of the approach depends on the context of the statistical tool that is meant to be used.

This question however is something that I  heard for the first time which can be re-phrased like this:

" I have computed the required sample size using Minitab however the resulting samples that I need to collect is much much more than the size of  the population under study? What would I do and what sample size would I take?"

There are several statistical theories to answer that, but being a practical person I lean towards the most simple to explain and the most simple to remember and works most of the time. This rule of thumb is known as Cochran’s (1977) correction factor. Basically the rule is:

If sample size is > than 3% of the population then use correction factor, otherwise use usual sample size computations.

The correction factor is a multiplier that is used to align the sample size to the population's size. It has the formula

C.F. = Initial_Sample_Size/(1 + Initial_Sample_Size/Population_Size)

Therefore the final sample size that an analyst should use whenever there is a limited population size is:

Final Sample  Size =  Initial_Sample_Size *Initial_Sample_Size/(1 + Initial_Sample_Size/Population_Size)