Question: Catheters. 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 that manufactures the catheter maintain a diameter of \(2.00 \mathrm{~mm}\). (The standard deviation is quite small.) Each day, quality control personnel make several measurements to test \(\mathrm{H}_{0}: \mu=2.00\) against \(\mathrm{H}_{\mathrm{A}}: \mu \neq 2.00\) at a significance level of \(\alpha=0.05\). If they discover a problem, they will stop the manufacturing process until it is corrected.

1. Is this a one-sided or two-sided test? In the context of the problem, why do you think this is important?
2. Explain in this context what happens if the quality control people commit a Type I error.
3. Explain in this context what happens if the quality control people commit a Type II error.

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