A college accepted new applicants, of whom 56% were male and 44% were female. The board of directors was not pleased that males were being accepted at a greater percentage than females. A private company investigated and found each department accepted a greater percentage of females over males. What may make this claim possible?

In Simpson paradox, the trend that appears in the combined data reverses or disappears in the results of the several individual groups that make up the combined data

In the question, given that the percentage of female applicants accepted = 44% while the percentage of male applicants = 56%, and that the private company found that each department accepted a greater percentage of females over males

The above claim can occur when there is a confounding variable, which is the number of applications from female or male

The percentage used or the data provided to by the private company in each department are percentage in proportion of number of accepted females to total number of female applicants and percentage in proportion of number of accepted males to total number of male applicants, whereby, when there are fewer number of female applicants to each department and more were accepted, their percentage will be larger than the percentage of the male applications that have a lower percentage but larger number of applications, such that the accepted male applicants still outnumber the female when that total number of applications are considered.