57. A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data supports the use of a one-sample t test.

a. What hypotheses should be tested if the investigators believe a priori that the design speci -

cation has been satis ed?

b. What conclusion is appropriate if the hypotheses of part

(a) are tested, t2.3, and a  .05?

c. What conclusion is appropriate if the hypotheses of part

(a) are tested, t1.8, and a  .01?

d. What should be concluded if the hypotheses of part

(a) are tested and t3.6?