Video Transcript
In an HR study about the salaries
in a certain company with 1,000 employees, the employees were divided into males and
females. If the total percentage of females
in the company was 60 percent and a sample of 40 people was selected, what was the
number of males in the sample?
Since the population, that is, the
employees in the company, naturally subdivides into two strata, that is, males and
females, we use stratified or layered random sampling as our sampling method. This means that any sample should
reflect the proportions of the strata within the population. Weβre told that 60 percent of the
employees were female. A sample of 40 people were
selected. And so 60 percent of those 40 must
be female.
Since the employees are split into
two distinct strata, male and female, if 60 percent are female, then 100 minus 60
percent must be male. That is, 40 percent of the
employees must be male. This in turn means that 40 percent
of the sample must also be male. And in order to calculate the
number of males in our sample, we use the formula π is equal to π percent times
π, where lowercase π is the stratum sample size. π is the stratum percentage of
population. And π is the overall sample
size. In our case then, the stratum size
for males is 40 percent times 40, which is the sample size, that is, 40 divided by
100 times 40.
Now we can divide both the
numerator and the denominator by 10. And once more, dividing numerator
and denominator by 10, we have in our numerator four multiplied by four, which is
16. The number of males therefore in
the sample is 16.
