Our agency believes that your company has engaged in hiring discrimination for supervisory positions at the welding gases
production facility. It has been brought to our attention that only one of the last 12 supervisors hired was female. Our
evidence shows that one-third of the applicants for supervisor positions were female, and one-third of 12 is four, so we
believe you have discriminated against female applicants. Please respond to this claim or have your legal counsel do so.
As you well know, there is no rule that we must hire women one-third of the time if they apply one-third of the time. There
are other factors that can explain any discrepancy in the proportion of female supervisors hired, such as the competition
from other employers or the specific credentials and brought by each applicant. Random chance, not malice, is responsible
for why one out of 12, rather than 4 out of 12, of our mostly recently hired supervisors was female.
We created a list of 300 hypothetical applicants, 200 male and 100 female. Then, we asked a computer to completely randomize
the numbers of the applicants and select 12 applicants at random. We recorded how many of the 12 were male and how many
were female in each trial. After 1,000,000 simulations, we tabulated how many trials led to 8 males hired, how many trials led to
9 males hired, etc., as summarized below:
As a result, we believe that the actual outcome in this case (11 males, 1 female) is not unlikely enough to warrant further
investigation into claims of discrimination, using the legal standard of 1% significance often imposed by the county court.
Number of Males Hired Number of Females Hired Frequency of Result 0 12 2 1 11 45 2 10 497 3 9 3,312 4 8 14,903 5 7 47,689 6 6 111,275 7 5 190,757 8 4 238,446 9 3 211,952 10 2 127,171 11 1 46,243 12 0 7,708
Consider each of the following statements. Does the information in the three sources support the inference as stated?
Based on the simulation, there is a probability of over 50% that at least eight of the new supervisors hired would be male.
If all 12 supervisors hired had been male, the county court would likely have supported a claim of discrimination against the company.
Considering just the trials in which less than half of the supervisors hired were male, only 1% of those trials would have been identified for possible discrimination against men using the county court’s legal standards.