Does anyone else share this odd facination: One of life's small joys for Alex is keeping a pen for long enough that you write all of the ink out of it.

A pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 h. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data sup- ports the use of a one-sample t test. (a) What hypotheses should be tested if the investigators believe a priori (aka ahead of time) that the design specification has been satisfied? (b) What conclusion is appropriate if the hypotheses of part (a) are tested, $t = -2.3$, and $\alpha = 0.05$? (c) What conclusion is appropriate if the hypotheses of part (a) are tested, $t = -1.8$, and $\alpha=.01$? (d) What should be concluded if the hypotheses of part (a) are tested and $t = -3.6$?