This isn't terribly common, but I had someone ask me "Would you rather fail to reject a hypothesis (when you should reject) or reject a hypothesis (when you shouldn't have)?" My immediate reaction to myself was "that's meaningless," because this wasn't an arena where you really have to worry; you just care about the results one way or another. But not knowing what to say, and not wanting to say what I thought of this question, I just shrugged my shoulders and picked one with a shake of my head and, what I'm sure was a look of confusion. I returned home afterwards and asked my former econometrics prof about it and her first response was "that question makes no sense." That was positively my worst interview ever. Hmm. That's not a terrible question for my field considering we rely on statistics for nearly every conclusion yet most, myself included, don't have a thorough understanding of it. If my null hypothesis is that this device or treatment we're developing is safe, I'd rather reject it (when I shouldn't have) than cause harm by failing to reject (when I should have).