The (entirely fictitious) University of South Central Maryland (USCM) is being sued for sexually discriminatory hiring practices. Last year, they hired two classes of employees: administrative staff and academic staff.
They received 750 applications from women for administrative staff positions, of which they hired 250, and 250 applications from women for academic positions, of which they hired 200.
In total, then, they had 1000 applications from women of which they hired 450, or 45%.
They received 300 applications from men for the administrative positions, of which they hired 75, and 700 applications from men for the academic positions, of which they hired 550. In total, of the 1000 applications they received from men, they hired 625, or 62.5%.
The question here is, is there any merit for the law suit based on the numbers?
Let us test statistically the claim on whether there is sex (men/women) discrimination or not.
p1 = 0.45, n1 = 1000
p2 = 0.625, n2 = 1000 = ...