I am teaching the OCR spec for the new A-Level and was looking through their back catalogue of S2 past papers to find some suitable hypothesis testing exam standard questions for the mean of a Normal distribution. I found one question which colleagues tell me has appeared in different guises in the past (with the characteristic phrase "not more than"): --------------------------- -------------------- I understand what OCR have done in their solution, but I disagree with it (and am asking/challenging you to argue against what I say below). I argue that the critical region is in the left hand tail. Solution #1 OCR's solution involves these ideas: H0: mu = 30 [the hypothesis that the computer specification is being met] H1: mu > 30 This leads to their answer of a critical region of tbar>32.6. Solution #2 The "wrong" solution, which OCR highlight in the examiner's report, is this: H0: mu = 30 H1: mu < 30 [the hypothesis that the computer specification is being met] This leads to the "wrong" answer of a critical region of tbar<27.4 My argument for solution #2 to the original question is as follows: (a) If the original question had instead stated that the computer specification is that the population mean time should be "less than 30 seconds" then the appropriate solution would be solution #2. (b) When dealing with continuous data (as we are here) "less than 30 seconds" means precisely the same thing as "not more than 30 seconds" (i.e. the wording used in the question). (c) Therefore, solution #2 is the appropriate solution to the original question. If the computer specification had stated "there should be no evidence that the population mean time is more than 30 seconds" then I would agree with OCR's solution #1. But that is not what is meant by the words they used ("the population mean time should not be more than 30 seconds"). I would be grateful if you would prove me wrong, or else agree with me. If you think I am wrong, which part of the argument (a)-(c) do you disagree with?