This depends crucially on the definition of "common sense." What is demonstrated by current research is that the form of cognition known as "rationality" is NOT well correlated with IQ (usually called "intelligence" by psychologists).

http://www.project-syndicate.org/commentary/stanovich1

The recent book-length work on this subject

http://www.amazon.com/What-Intelligence-Tests-Miss-Psycholog...

http://yalepress.yale.edu/yupbooks/book.asp?isbn=97803001238...

provides abundant references to peer-reviewed experimental literature on this distinction.