Testing the above theory is somewhat intimidating. The theory leads to many hypotheses. If a member provides more federal programs for their district, they are more likely to get re-elected Committees are able to block any legislation they dislike. If a Member is on a Committee, other Members who want to get bills through the committee will add measures that benefits the Committee members' districts. Therefore members of important committees will have more federal spending on their districts.
Representatives are more likely to be on committees that can benefit their constituents.
To fully test the theory, you would have to test all of these hyppotheses, and maybe more. This is beyond the scope of your project. You decide to test just the last hypothesis. If this is not the case, then that is a serious blow to the theory. You have to decide how to operationalize your hypotheses.