Chapter 21, Problem 32E

(a)

To determine

To find out what is the null and alternative hypotheses.

Explanation of Solution

It is given in the question that you are in charge of shipping computers to customers. You learn that a faulty disk was put into some of the machines. Thus, the null hypothesis states that the drive in the computer is good. And the alternative hypothesis states the opposite, so, it is that the drive in the computer is bad.

(b)

To determine

To explain what would you decide given that a computer fails the test and what if it passes the test.

Explanation of Solution

It is given in the question that you are in charge of shipping computers to customers. You learn that a faulty disk was put into some of the machines. Thus, the null hypothesis states that the drive in the computer is good. And the alternative hypothesis states the opposite, so, it is that the drive in the computer is bad. Thus, we would decide given that a computer fails the test that we will reject the null hypothesis and if the computer passes the test then we fail to reject the null hypothesis.

(c)

To determine

To explain how large is $\alpha$ for this test.

Answer to Problem 32E

  $4\%$ .

Explanation of Solution

It is given in the question that you are in charge of shipping computers to customers. You learn that a faulty disk was put into some of the machines. Thus, the null hypothesis states that the drive in the computer is good. And the alternative hypothesis states the opposite, so, it is that the drive in the computer is bad. Thus, $\alpha$ will be $4\%$ because it is given in the question that there is a $4\%$ chance a good drive will fail.

(d)

To determine

To explain what is the power of this test.

Answer to Problem 32E

  $65\%$

Explanation of Solution

It is given in the question that you are in charge of shipping computers to customers. You learn that a faulty disk was put into some of the machines. Thus, the null hypothesis states that the drive in the computer is good. And the alternative hypothesis states the opposite, so, it is that the drive in the computer is bad. Thus, the power of the test will be $65\%$ because bad drive fail $65\%$ of the time, as,

  $\begin{array}{l}\text{Power}=1-0.35\\ =0.65\end{array}$