<p>A very thought-provoking question.</p>
<p>There are two problems with it. The first is not so important but worth pointing out. Art of Problem Solving is a little too easy, at least for many Techers who like math. And not all Techers like pure cleverness-oriented math puzzles. You'd have to pick the "math/science" treatment to be a "fun" academic activity at the level of each individual Techer. So for math Olympiad types it could be Putnam exam problems, and for engineering types it could be building your own GPS device from scratch. But a decent approximation would be to consider one major for this study, say EE, and pick an activity that most EE people would get excited about at least in principle.</p>
<p>More importantly, even after we do that, your study is not at all the right one to get at the thing you want to figure out. You want to estimate interest/passion/obsession, but the results will depend a lot more on self-control than on those things. The choice you should be giving these kids (and maybe this is what you were intending) is as follows:</p>
<p>Would you be willing to commit to doing at least x hours of [fun academic activity] per week for the summer? Or would you prefer not to commit to anything and to have free time to do whatever you want, like playing Halo 3?</p>
<p>"Commit" here means "agree to do something or be punished." The punishment can be something like being exiled to North Dakota for a year.</p>
<p>Without commitment, you would observe a majority of Techers playing Halo not because they really prefer that, in a reflective way, to doing math and science, but because they lack the self control to always do the things that they "really, in a deep and long-term way" want to do. (Hence, you observe me posting on this message board.) By giving the option to commit to something, you find out what their rational, long-term selves really want. In this case most if not all Techers would pick a pretty high x, say over 60 hours a week.</p>
<p>How do I know this? Every single person who agreed to go to Caltech committed to four years of the most intense math and science bootcamp in the country; if they fail to put in a lot of time working, they'll fail out and have to restart their educations, which may be quite hard, and is likely to be much worse than North Dakota. That is, we already ran the experiment, and by definition, all Techers are in the "obsessed" category. So, after the study is amended so that it elicits what you intend to elicit, 100% of Techers are in your category (1).</p>