Comment by PeterisP

Regarding the second part, yes, the fact that academic achievement is highly influenced by socioeconomic status is well supported by research; a big part of the whole correlation is that higher socioeconomic status means better schools, but there's still a strong effect within the same school. There's a bunch of studies that try to estimate the nature/nurture split, but in any case higher socioeconomic status correlates positively with pretty much everything schooling-wise.