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.