Are you accidently mis-stating this? You seem to be saying that a higher percentage of kids in diverse schools (71%) "believed their parents would not approve of inter-racial friendships", whereas [only] 47% of kids in "majority white schools "believed their parents would not approve of inter-racial friendships". These statements of yours are the opposite of the earlier statement that "schools that have a decent mix of black and white children display more optimism". I think you forgot about the "not" in that sentence and mis-stated things here. Perhaps you should re-write?