Two coins In a drawer are two coins. They look thesame, but one coin produces heads 90% of the time whenspun while the other one produces heads only 30% ofthe time. You select one of the coins. You are allowed tospin it once and then must decide whether the coin is the90%- or the 30%-head coin. Your null hypothesis is thatyour coin produces 90% heads.a) What is the alternative hypothesis?b) Given that the outcome of your spin is tails, whatwould you decide? What if it were heads?c) How large is a in this case?d) How large is the power of this test? (Hint: How manypossibilities are in the alternative hypothesis?)e) How could you lower the probability of a Type I errorand increase the power of the test at the same time?

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Q: P(1)=.25 P(2) & P(3) =.2 P(4)=.05 P(5)= .1 P(6)= .2

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2-Proportion Test

In a 2-proportion test, two separate proportions are measured at the same time, and their similarity is evaluated. It is also known as a 2-proportion z-test, and a comparison of two different proportions is done in this method.