Q$34.$ Production managers on an assembly line must monitor the output to be sure that the level of defective products remain small. They periodically inspect a random sample of items produced. If they find a significant increase in the production of items that must be rejected, they will halt the assembly process until the problem can be identified and repaired.

Q$36.$ Consider again the task of the quality control inspectors in exercise $34.$

a$)$ In this context, what is meant by the power of the test the inspectors conduct?

b$)$ They are currently testing $5$ items each hour. Someone has proposed that they test $10$ instead. What are the advantages and disadvantages of such a change?

c$)$ Their test currently uses a $5\%$ level of significance. What are the advantages and disadvantages of changing to an alpha level of $1\%?$

d$)$ Suppose that, as a dasses, one of the machines on the assembly line produces more and more items that are defective. How will this affect the power of the test?