Faulty or not? You are in charge of shipping computers to customers.

You learn that a faulty chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of the bad chips pass the test, too. You have to decide on the basis of one test whether the chip is good or bad. Make this a hypothesis test.

a) What are the null and alternative hypotheses?

b) Given that a computer fails the test, what would you decide?

What if it passes the test?

c) How large is a for this test?

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