Let p denote the portion of a student’s exam with errors. Suppose we test H0 : p = 0.05 and Ha : p > 0.05 using the following rule. Two problems are chosen at random. If both are error free, we reject H0. If one or both contains an error, we look at a third problem. If the third problem is error free, we reject H0. In all other cases, we accept H0.

(a) Explain type I error in the context of this problem.

(b) What is the value of ? associated with this test?

(c) Explain type II error in the context of this problem.

(d) Calculate ? = Pr(type II error) as a function of p.