Let's say I have a given sample population $P$, that describes the traits of a group of people as a predictor variable, and whether or not they are CEOs as a response variable. I am trying to determine using a decision tree whether or not females are being discriminated against. That is, all else being equal, being a woman makes you less likely to be a CEO.
Would this fall under the category of inferential or descriptive statistics.
I am of two schools of thought here...
Descriptive: I have two distributions, male and female. I would like to see if all else equal, females have a lower "CEO rate". This seems like I'm describing the data.
Inferential: The way I would do this, is that I would make a decision tree and look at how it breaks up the data. In order to check and see if this tree is not overfitting, I would need to use test data results. This leads me to believe it is an inferential problem.
I am leaning more towards the latter, but I do not have enough experience to definitively say it is one or the other. Thoughts?