Teachers truly believe that studying increases academic performance, but measuring the relationship between grades and studying is a difficult task. One cannot simply observe the correlation between hours spent studying and grades because that raw correlation does not hold other important variables constant. Such correlations are influenced by these other variables, making the correlations difficult to interpret.
For example, students naturally interested in economics will both pay more attention in class and study longer for economics classes. In all probability, they will make higher grades as well. If we detect a positive correlation between their higher grades and longer study hours, what really caused the higher grades: the longer study hours or the greater attention paid in class?
To truly measure the impact of studying, some sort of experiment - natural or unnatural - is needed where an exogenous, random event alters the study habits of a random group of students. A recent article in the B.E. Journal of Economic Analysis Policy contains such an experiment.
A particular Kentucky university requires all incoming students to live in a dormitory and assigns them roommates at random. Some of these roommates happen to bring video games with them. It turns out that a student whose randomly selected roommate brings a video game tends to study less. Thus, if the students whose roommate brought a video game to school performed worse academically, studying really does improve grades - everything else held constant.
The study tested whether a grade difference exists between these students and those whose roommates did not bring a video game, and the latter group did perform better.
Bottom Line: it is proven, studying improves performance, regardless of what kind of student you happen to be!