It’s eight o’clock Saturday morning and our daughter Kenzie is back at the high school taking the PSAT. The SAT, or Scholastic Aptitude Test, is the standardized entrance exam used by most U.S. universities as part of their admissions criteria. This is the pre-SAT: a practice version of the real thing taken by many if not most college-bound high school juniors. The fact that Kenzie and most of her pals, only sophomores, are sitting over there taking the test has to say something. I don’t believe that Anne and I drove her to it, but we didn’t dissuade her either. Hey, it’ll be fun, I told her the other day as she was deciding at the last minute whether or not to sign up. I happen to find these tests amusing and I suspect she does too, since in her free time she often tracks down mini-IQ tests on the internet and reports her results to us.
Should you guess if you don’t know the answer to a question? This was the focus of the family breakfast discussion this morning. I said yes, but then we wondered whether the test scorers simply count up the right answers or if they impose a penalty for wrong answers. Anne did a quick internet search, and it turns out there is a penalty for mistakes. But how big a penalty? The testers’ recommendation: if you can eliminate one or more options, guess; if you can’t, then leave the question blank. So let’s say each multiple-choice question presents 4 options from which to choose: if you guess randomly you have a 25% chance of getting it right. If you can eliminate one clearly wrong answer then you choose from the remaining 3 options, leaving you with a 33% chance of guessing correctly. That means the penalty must be somewhere between 0.25 and 0.33 per wrong answer. Problem solved.
But this formulation of the problem seems awfully logical, awfully Bayesian in its solution space. What if you’ve just got a feeling that one of the answers might be right? Should you go with your instinct, your gut, the vibe coming at you from the test booklet?
(c) only after you’ve eliminated any obviously wrong responses
(d) it depends
For extra credit please explain your answer.