I have a large dataset (https://www.kaggle.com/teejmahal20/airline-passenger-satisfaction) regarding airline passenger satisfaction. I applied a decision tree on this dataset and I extracted the feature importance and it seems that the quality of the inflight wifi service is the best predictor for the final satisfaction level of the passengers. Please keep in mind that the target variable is binary in this dataset (satisfied or dissatisfied).
I would like to cross-check this result by using "classical" statistics - hypothesis testing - whether the quality / level of satisfaction with respect to the wifi service is really a good indicator of whether the passenger will be satisfied or not. The final purpose of my research is to create an algorithm that can provide quality information for a business decision making process from the airlines' point of view (is it worth to invest in X service in order to improve our passenger's satisfaction level? - if the quality of the service is improved by a% then b% of the passengers become satisfied and are more likely to fly with our airline again).
I've identified the PSM (propensity score matching) as a way to "create" these control & test group for my hypothesis, but I'm not sure how to apply this or whether it is what I am really looking for.
Can anyone shed some light into this problem? Any help with respect to properly selecting a control group and a test group for this hypothesis testing will be greatly appreciated!
Many thanks!