Quality are reliability are becoming important aspects of computer hardware and software. Past experience shows that the probabiltiy of failure during the first 1000 hours of operation for 16-kbit dynamic RAM produced by a United States firm is .2. It is hoped that new technology and stricter quality controls have reduced this failre rate. To verify this contention, 20 systems will be monitored for 1000 hours and the number of failures ill be recorded.

A) Set up the appropriate null and alternative hypotheses.

B)Explain in a practical sense the consequences of making a Type 1 and a Type 2 error.

C) If Ho is true and p=.2, what is the expected numbers of failures during the first 1000 hours in the 20 trials?

D) Let us agree to reject Ho in favior of H1 if the observed number of failures, X, is at most 1. In this way we are presetting ? at what level?

E) Suppose that it is essential that the test be able to distinguish between a failure rate of .2 and a failure rate of .1. Fine the probability that the test as designed will be unable to do so. That is, Find ? if p=.1. Find the power of the test if p=.1.