Faulty or not? A machine is used in a quality control process to select the faulty items

Question:

Faulty or not? A machine is used in a quality control process to select the faulty items in a production line.

The machine is not 100% ideal in which 11% of faulty items will not be selected by the machine and overall, 1%

of functioning items will be selected by the machine as a faulty item. Thus, the workers have to manually recheck the selected items to see whether the item is faulty or not.

Make this a hypothesis test.

a) What are the null and alternative hypotheses?

b) Given that the machine works ideally, what would you decide? What if it does not work ideally?

c) How large is a in this test?

d) What is the power of this test? (Hint: How many possibilities are in the alternative hypothesis?)

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