Chapter PV, Problem 33RE

(a)

To determine

To state the null and alternative hypothesis.

Answer to Problem 33RE

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

Explanation of Solution

It is given in the question that a computer company recently experienced a disastrous fire that ruined some of its inventory. Each computer goes with a series of tests. Thus, the null hypothesis is that there is no difference in the damaged and undamaged computers and the alternative hypothesis is that there is difference in the damaged and undamaged computers. So, we define hypotheses as:

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

(b)

To determine

To discuss the advantages and disadvantages of this test plan.

Explanation of Solution

It is given in the question that a computer company recently experienced a disastrous fire that ruined some of its inventory. Each computer goes with a series of tests. So, we define hypotheses as:

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

Thus, as someone suggests classifying a computer as damaged if it fails any of it fails any of the tests so, the advantages are that no damaged computers will be classified as good and the disadvantages is that some good computer will be categorized as damaged.

(c)

To determine

To find out what number of tests would a computer have to fail in order to be classified as damaged if the engineers want to have the probability of a Type I error equal to $5\%$ .

Answer to Problem 33RE

Three number of tests.

Explanation of Solution

It is given in the question that a computer company recently experienced a disastrous fire that ruined some of its inventory. Each computer goes with a series of tests. So, we define hypotheses as:

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

Thus, we can say that $3$ number of tests would a computer have to fail in order to be classified as damaged if the engineers want to have the probability of a Type I error equal to $5\%$ because undamaged is five computers for more than two failed tests as given in the table.

(d)

To determine

To find out what is the power of test plan in part (c).

Answer to Problem 33RE

The power of test is $20\%$ .

Explanation of Solution

It is given in the question that a computer company recently experienced a disastrous fire that ruined some of its inventory. Each computer goes with a series of tests. So, we define hypotheses as:

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

Thus, for three or more failed tests, the power of test plan in part (c) will be $20\%$ .

(e)

To determine

To explain the statement given.

Explanation of Solution

It is given in the question that a computer company recently experienced a disastrous fire that ruined some of its inventory. Each computer goes with a series of tests. So, we define hypotheses as:

  $\begin{array}{l}{H}_0:\text{Computer is undamaged}\\ H_a:\text{Computer is damaged}\end{array}$

Suppose a colleague points out that by increasing $\alpha \text{ just 2\%}$ the power can be increased substantially, this means that it moves the cut-off to two or more failed tests which increases power to $90\%$ .