Testing The Equality of Two Exponential Population Distributions. The Reliable Computer Co. is considering purchasing CPU chips from one of two different suppliers to use in the production of personal computers. It has two bids from the suppliers, with supplier number offering the lower bid. Before making a purchase decision, you want to test the durability of the chips, and you obtain a random sample of 50 chips from each supplier. It is known that both CPUs have operating lives that are exponentially distributed, and you want to test the equality of the expected operating lives of the chips.

(a) Define a size 10 test of the equality of the means of the two population distributions, i.e., a test, of \(H_{0}: \theta_{1}\) \(=\theta_{2}\) versus \(H_{a}\) : not \(H_{0}\).

(b) The respective sample means of operating lives for the two sample were \(\bar{x}_{1}=24.23\) and \(\bar{x}_{2}=18.23\). Conduct the test of the null hypothesis. Does the test outcome help you decide which supplier to purchase chips from?

(c) How would your test rule change if you wanted to test a one-sided hypothesis concerning the means of the population distributions?

(d) Consider using the LM test procedure for this problem. What is the test rule? Can you perform the test with the information provided?

(e) Consider using the WALD test procedure for this problem. What is the test rule? Can you perform the test with the information provided?