To test the ability of mechanics to identify simple engine problems, a car with a single such

problem was taken in turn to 72 different car repair facilities. Only 42 of the 72 mechanics who

worked on the car correctly identified the problem. Does this strongly indicate that the true proportion of mechanics who could identify this problem is less than 0.75?


a) Perform the appropriate test of hypothesis using = 0.01. Clearly show the eight (8) steps

of hypothesis testing, draw a picture of the rejection region, and include the p-value. (10)


b) Interpret a Type I error in terms of this example. (2)


c) What is the probability of making a Type I error in this example. (2)


d) Find the probability of making a Type II error in this example, given = 0.745. Suppose the rejection region is p^< 0.74. (5)

e) Interpret the probability of a type II error in terms of this example.