During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient's leg. It's important that the company who manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation is quite small.) Each day, quality control personnel make several measurement to test H₀: = 2.00 against H_A: 2.00 at a significance level of = 0.05. If they discover a problem, they will stop the manufacturing process until it is corrected.

A) Is this a one-sided or two-sided test? In the context of the problem, why do you think this is important?

B) Explain in this context what happens if the quality control people commit a Type I error and explain the implications.

C) Explain in this context what happens if the quality control people commit a Type II error and explain the implications.

Suppose that the catheter company is reviewing its testing procedure.

D) If the significance level is changed to = 0.01 will the probability of Type II error increase, decrease, or remain the same?

E) What is meant by the power of the test the company conducts?

F) Suppose the manufacturing process is slipping out of proper adjustment. As the actual mean diameter of the catheters produced gets farther and farther above the desired 2.00 mm, will the power of the quality control test increase, decrease, or remain the same?

G) What could this company do to improve the power of the test?