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 fail to reject H0. (a) Explain type I error in the context of this problem. (b) What is the value of α associated with this test? (c) Explain type II error in the context of this problem. (d) Calculate β = P(type II error) as a function of pa, i. e find the value of β(pa) where pa > 0.05.