Chapter 23, Problem 26E

(a)

To determine

To find out is this aone-sided or two-sided test and explain why do you think this is important.

Answer to Problem 26E

It is a two-sided test.

Explanation of Solution

In this question, during an angiogram, heart problems can be examined via a small tube threaded into the heart from a vein in the patient’s leg. It is important that the company that manufacturers the catheter maintain a diameter of $2$ mm. It is also given that,

  $\begin{array}{l}{H}_0:\mu =2\\ H_1:\mu \ne 2\end{array}$

  $\alpha =0.05$

By this, we know that if the alternative hypothesis contains $\ne$ , then the test is two-sided.

And if the alternative hypothesis contains $>$ or $<$ , then the test is one sided..

Thus, according to the information, it is a two-sided test. This is important because the catheter needs to maintain a diameter of $2$ mm.

(b)

To determine

To explain what will happen if the quality control commit a Type I error.

Explanation of Solution

In this question, during an angiogram, heart problems can be examined via a small tube threaded into the heart from a vein in the patient’s leg. It is important that the company that manufacturers the catheter maintain a diameter of $2$ mm. It is also given that,

  $\begin{array}{l}{H}_0:\mu =2\\ H_1:\mu \ne 2\end{array}$

  $\alpha =0.05$

Now, if the inspectors commit a Type I error then Type I error means reject the null hypothesis, when it is true. Thus, it means that they will decide that the quality is bad while the quality is good.

(c)

To determine

To explain what will happen if the quality controlcommit a Type II error.

Explanation of Solution

In this question, during an angiogram, heart problems can be examined via a small tube threaded into the heart from a vein in the patient’s leg. It is important that the company that manufacturers the catheter maintain a diameter of $2$ mm. It is also given that,

  $\begin{array}{l}{H}_0:\mu =2\\ H_1:\mu \ne 2\end{array}$

  $\alpha =0.05$

Now, if the inspectors commit a Type II error then Type II error means fail to reject null hypothesis when it is false. Thus, it means that they will decide that the quality is good when the quality is bad.