Following our CFA exam example, the researchers could take a sample of 1,000 CFA participants
from the total 200,000 test sitters and run the required data on this number.
The total number of students in a city can be taken as a population, and the total number of dogs in a city is also a population size.
This means that if the sample mean of the 1,000 CFA exam participants is 50, the
population mean of the 200,000 test takers should also be approximately 50.
However, in a case where it will be insightful to know the ratio of men to women
that passed the test after studying for less than 40 hours, using a stratified random sample would be preferable to a simple random sample.
In fact, by the time the data from the population has been collected
and analyzed, a couple of years would have passed, making the analysis worthless since a new population would have emerged.
The random sample drawn from the population should therefore, have 400 women and 600 men for a total of 1,000 test takers.
From a population of 200,000 test takers that sat for the exam in 2016, 40% were women and 60% were men.
With a stratified random sample, these fractions are a mini-representation of the population
and simulates the population’s characteristics better than a simple random sample.