When a thread-cutting machine is operating properly, only 2% of the units produced are defective. Since the machine was bumped by a forklift truck, however, the quality-control manager is concerned that it may require expensive downtime and a readjustment. The manager would like to set up a right-tail test at the 0.01 level of significance, then identify the proportion of defectives in a sample of 400 units produced. His null hypothesis is H0:  # 0.02, with H1:  . 0.02.

a. What critical value of z will be associated with this test?

b. For the critical z determined in part (a), identify the sample proportion that this z value represents, then use this value of p in stating a decision rule for the test.

c. What is the probability that the quality-control manager will fail to reject a false H0 if the actual population proportion of defectives is  5 0.02? If

 5 0.03? If  5 0.04? If  5 0.05? If  5 0.06?

d. Making use of the probabilities calculated in part (c), plot the power and operating characteristic curves for the test.