Does anyone know what studies is referred to, because I can't find anything...
Based on the lack of details, probably it's either made up, not reputable, obsolete to the bone, a lie, a study conducted by themselves, focused on something completely unrelated, or any combination of the above.
Why a study from the 40's? Psychology and the way we understand and interpret human behavior has changed quite a lot since the 40s.
Also, I did a simple google search on the matter, and found quite a few articles on psychology that, to my surprise, do the exact same thing. They say things like "Studies demonstrate that exercising willpower makes heavy demands on mental energy..." without citing the source.
Hmm... now I'm curious about the psychology of self control.