Chapter 23, Problem 27E

(a)

To determine

To explain if the company’s lawyers are worried about being sued for selling an unsafe product should they increase or decrease the value of $\alpha$ .

Answer to Problem 27E

It will decrease.

Explanation of Solution

It is given in the question that the manufacturer of the metal TV stands in previous exercise is thinking of revising its safety test. Thus, we have that,

  $\begin{array}{l}{H}_0:\mu =500\\ H_1:\mu >500\\ \alpha =0.01\end{array}$

The Type I error states that reject null hypothesis when it is true. This interprets that the inspectors will decide that the stands are safe while the standards are not safe. And the Type II error is that when we fail to reject the null hypothesis when it is false. This interprets that the inspectors will decide that the stands are unsafe while the standard are safe. The Type I error is the worst because the stands are not safe. We then should decrease $\alpha$ because $\alpha$ is the probability of making a Type I error.

(b)

To determine

To explain what is meant by the power of test.

Explanation of Solution

It is given in the question that the manufacturer of the metal TV stands in previous exercise is thinking of revising its safety test. Thus, we have that,

  $\begin{array}{l}{H}_0:\mu =500\\ H_1:\mu >500\\ \alpha =0.01\end{array}$

The power of test is the probability to reject the null hypothesis when null hypothesis is false. Thus, we interpret from that the probability of deciding that the stands are safe when the stands are actually safe.

(c)

To determine

To explain the advantages and disadvantages of each option.

Explanation of Solution

It is given in the question that the manufacturer of the metal TV stands in previous exercise is thinking of revising its safety test. Thus, we have that,

  $\begin{array}{l}{H}_0:\mu =500\\ H_1:\mu >500\\ \alpha =0.01\end{array}$

If we increase the sample size then the advantage of this is the increase in the power and the disadvantage of this is that it is more costly and very time consuming. If we decrease the standard deviation then the advantage is that it increases the power and the disadvantage is that it becomes more costly. Now, if we increase $\alpha$ then the advantage is that it will increase the power and the disadvantage of this will be that it is of more Type I errors and thus more likely to be sued for selling an unsafe product.