It will surprise you not at all to hear that students from higher income families get higher SAT scores. Here’s a picture of the 2013 facts.
Unless you’ve recently been in the college hunt, you may not have a good idea of how many points should be thought of as making a “big difference” on the SAT. So I’ve add to the graph very approximate average SAT score of admitted students at Cal State Long Beach, a very good university in California’s second academic tier, and UCLA–one of the world’s better public universities. (Please don’t try to read the graph backwards. This doesn’t give you average family income at these schools.)
The SAT scores at Cal State Long Beach correspond to typical scores from a kid from a fairly well-off, middle class family. Maybe an upper middle-class family. The scores at UCLA are off the chart (literally off the chart).
The lesson lies at the left end of the chart. Typical scores from the lower end of the income distribution aren’t going to get a student into any competitive four-year university.