I must be in a Yale mood. One of the first google hits was this from Yale NROTC FAQ:
Do I have to major in some particular subject if I join the NROTC?
It depends. In an increasingly technical Navy, scholarship preference is now given to students who major in technical fields (Tier 1 and 2 majors), with 85% of all scholarships going to those students. Additionally, scholarships are awarded to a specified tier, and in order to maintain your scholarship eligibility you need to maintain a major within that tier. Students who wish to change tiers must have prior approval from the Commanding Officer or Naval Service Training Command as appropriate (see below). College Program students can enter the program with any major, but if awarded a scholarship it will be for a specific tier.