Chapter 21, Problem 26E

(a)

To determine

To explain is this a one-tailed or a two-tailed test and why.

Answer to Problem 26E

It is a one-tailed test.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Thus, from this context we can say that it is a one-tailed test because we are only interested in whether or not they are more visible. If the design makes the signs less visible, we don't really care how much less visible it becomes..

(b)

To determine

To explain what would a Type I error be.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers.Thus, in this context a Type I error would be defined as deciding that the signs are more visible when they are actually not.

(c)

To determine

To explain what would a Type II error be.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Thus, in this context a Type II error would mean that failing to decide that the signs are more visible when they actually are.

(d)

To determine

To explain what is meant by the power of the test.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers.Thus, in this context the power of the test means that the probability of correctly detecting that a more visible sign actually works.

(e)

To determine

To explain how will this affect the power of the test.

Answer to Problem 26E

It will decrease.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers.Thus, in this context the power of test will be affected as it will decrease the power because we will need more evidence to reject the null hypothesis. And the power is $1-\beta$ and $\beta$ decreases as $\alpha$ increases. Therefore, a higher $\beta$ means lower power.

(f)

To determine

To explain how would this affect the power of the test.

Answer to Problem 26E

The power of the test will be lower.

Explanation of Solution

It is given in the question that highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers.Thus, we can say that the power of the test will be lower because as the sample size will be smaller and thus the power of the test will also be lower.