8. When 30 transistors were simultaneously put on a life test that was to be terminated when the 10th failure occurred, the observed failure times were (in hours) 4.1, 7.3, 13.2, 18.8, 24.5, 30.8, 38.1, 45.5, 53, 62.2. Assume an exponential life distribution.

(a) What is the maximum likelihood estimate of the mean life of a transistor?

(b) Compute a 95 percent two-sided confidence interval for the mean life of a transistor.

(c) Determine a value c that we can assert, with 95 percent confidence, is less than the mean transistor life.

(d) Test at the α = .10 level of significance the hypothesis that the mean lifetime is 7.5 hours versus the alternative that it is not 7.5 hours.