Chapter 21, Problem 27E

(a)

To determine

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

Answer to Problem 27E

It is a one-tailed test.

Explanation of Solution

It is given in the question that a statistics professor has observed that for several years about $13\%$ of the students who initially enrol in his introductory statistics course withdraw before the end of the semester. Thus, by this context we can say that it is a one-tailed test because software is supposed to decrease the dropout rate. We do not want it to increase.

(b)

To determine

To write the null and alternative hypotheses.

Answer to Problem 27E

  $\begin{array}{l}{H}_0:p=0.13\\ H_a:p<0.13\end{array}$

Explanation of Solution

It is given in the question that a statistics professor has observed that for several years about $13\%$ of the students who initially enrol in his introductory statistics course withdraw before the end of the semester. Thus, we can say that the null hypothesis states that the rate of students be equal to $13\%$ and the alternative hypothesis states that the rate of students be less than $13\%$ . So, we define hypothesis by:

  $\begin{array}{l}{H}_0:p=0.13\\ H_a:p<0.13\end{array}$

(c)

To determine

To explain what would happen if the professor makes a Type I error.

Explanation of Solution

It is given in the question that a statistics professor has observed that for several years about $13\%$ of the students who initially enrol in his introductory statistics course withdraw before the end of the semester. Thus, if the professor makes a Type I error then he buys the software when it doesn't actually help students.

(d)

To determine

To explain what would happen if the professor makes a Type II error.

Explanation of Solution

It is given in the question that a statistics professor has observed that for several years about $13\%$ of the students who initially enrol in his introductory statistics course withdraw before the end of the semester. Thus, if the professor makes a Type II error the he doesn't buy the software when it actually helps students.

(e)

To determine

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

Explanation of Solution

It is given in the question that a statistics professor has observed that for several years about $13\%$ of the students who initially enrol in his introductory statistics course withdraw before the end of the semester. Thus, in this context the power of the test means that the probability of correctly deciding that the software if helpful.