Question: Two coins. In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head coin. Your null hypothesis is that your coin produces 90% heads.

a) What is the alternative hypothesis?

b) Given that the outcome of your spin is tails, what would you decide? What if it were heads?

c) How large is in this case?

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

e) How could you lower the probability of a Type I error and increase the power of the test at the same time?