22. Suppose that the life distributions of two types of transistors are both exponential.

To test the equality of means of these two distributions, n1 type 1 transistors are simultaneously put on a life test that is scheduled to end when there have been a total of r1 failures. Similarly, n2 type 2 transistors are simultaneously put on a life test that is to end when there have been r2 failures.

(a) Using results from Section 14.3.1, show how the hypothesis that the means are equal can be tested by using a test statistic that, when the means are equal, has an F -distribution with 2r1 and 2r2 degrees of freedom.

(b) Suppose n1 = 20, r1 = 10 and n2 = 10, r2 = 7 with the following data resulting.

Type 1 failures at times:

10.4, 23.2, 31.4, 45, 61.1, 69.6, 81.3, 95.2, 112, 129.4 Type 2 failures at times:

6.1, 13.8, 21.2, 31.6, 46.4, 66.7, 92.4 What is the smallest significance level α for which the hypothesis of equal means would be rejected? (That is, what is the p-value of the test data?)