Even though Correlation doesn't imply causation. And I am sure the rich on average are more astute than the poor. I believe the gap is exaggerated by parenting and outlook.

Anecdote: I was poor and the first person in my family to go to college. Even though I was taking the SAT and several stem AP classes I still didn't truly think I was going to college. I was just going through the motions.

A few months before I graduated HS our family lost our home and we were being evicted soon. I didn't think college was possible. I thought I was going to have to work full time for minimum wage to support my mom and siblings. I Ended up only studying for the SAT the day before. I scored somewhat average. 650 math, 500 verb and 550 writing.

I ended up going to a local state university and worked part time. I graduated with a BSEE. I just took the GRE and really studied, I scored 169 quantitative and 166 verbal.

It should be noted that my resolve only changed after my situation improved so it is possible that without a solid foundation in the home most teens won't study like they should.