Spin Off Logic Problem From Genius-Religion Debate

[TomCowley]

The problem can be restated with only the trivially necessary stipluations, namely that there is a statistically meaningful correlation between IQ and belief in Y, and that the sampling method is robust enough to ensure confidence (90%, 95%, 99%, whatever) that the correlation is to IQ and not to a confounding factor also correlated to IQ. Is such a correlation enough to believe (with roughly the same confidence you have in the data) Y is true, even if the highest IQ group surveyed is only 30% to believe Y?