...do not go hand in hand. Rich people have a privileged access to the best Universities, as this interesting study in the NYRB confirms.
here's an excerpt:
The causes and consequences of these dispiriting facts are complex, and the cost to society—moral and material—is high. There is moral cost in the shortfall between the professed ideal of equal opportunity and the reality of rising inequality. As for the material cost, "there has never been reason to believe that all outstanding candidates will be able to pay whatever fees are charged without help," as Bowen and his colleagues put it, and "society at large needs all the trained talent it can marshal."