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? 3.1 Perform the appropriate test of hypothesis using ? = 0.01. Clearly show the seven (7) steps of hypothesis testing, draw a picture of the rejection region, and include the p-value. 3.2 Interpret a Type I error in terms of this example. 3.3 What is the probability of making a Type I error in this example. 3.4 Determine whether the test procedure in 3.1 is indeed valid.
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?
3.1 Perform the appropriate test of hypothesis using ? = 0.01. Clearly show the seven (7) steps
of hypothesis testing, draw a picture of the rejection region, and include the p-value.
3.2 Interpret a Type I error in terms of this example.
3.3 What is the probability of making a Type I error in this example.
3.4 Determine whether the test procedure in 3.1 is indeed valid.
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