AshwinSundar, I'd say that if you had any trouble understanding any of the concepts in AP Stat, or applying them properly in context, I couldn't recommend the Caltech environment to you.
On the other hand, if you read the AP Scoring Guides, there are a lot of ways to lose points on the AP Stat exam which do not reflect on your ability--in fact, to the contrary. For example, in your answer, you often have to repeat a statement about the nature of the sample which is one of the "givens" in the question, or you lose points for that (well, ok that's in the nature of proof). But if there is an assumption in the application of a statistical test that the sample is 10% or less of the entire population (say), and you are given the information that the entire population is 600 and the sample size is 50, you have to actually write down that 10% of 600 is 60 and 50 < 60. Saying that 50 is less than 10% of 600 will actually not get you all of the points . . . . absurd, but I'm pretty sure it's true. A test-savvy teacher or self-studier will look at the scoring guides for the free response, which are posted on the CB web site. So, did your teacher mention some of the weirdness in the free response expectations, or not?