Chapter 23, Problem 6E

(a)

To determine

To explain which conclusion is correct and also what is wrong with others.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given that software analysis of the salaries of a random sample of $288$ Nevada teachers produced the $90\%$ confidence interval for the mean $\mu$ . The first conclusion is: If we took many random samples of $288$ Nevada teachers, about $9\text{ out of 10}$ of them would produce this confidence interval. This conclusion is incorrect because almost all random samples will result in different confidence intervals and thus it is not possible that $9\text{ out of 10}$ have the same confidence interval.

(b)

To determine

To explain which conclusion is correct and also what is wrong with others.

Answer to Problem 6E

It is correct.

Explanation of Solution

It is given that software analysis of the salaries of a random sample of $288$ Nevada teachers produced the $90\%$ confidence interval for the mean $\mu$ . The second sample is: If we took many random samples of Nevada teachers, about $9\text{ out of 10}$ of them would produce a confidence interval that contained the mean salary of all Nevada teachers. This conclusion is correct because $90\%$ of all possible sample will have a confidence interval that contains the population mean.

(c)

To determine

To explain which conclusion is correct and also what is wrong with others.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given that software analysis of the salaries of a random sample of $288$ Nevada teachers produced the $90\%$ confidence interval for the mean $\mu$ . The third conclusion is: About $9\text{ out of 10}$ Nevada teachers earn between $\$38944\text{ and \$42893}$ . This conclusion is incorrect because the given confidence interval is for the population mean and not for individuals.

(d)

To determine

To explain which conclusion is correct and also what is wrong with others.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given that software analysis of the salaries of a random sample of $288$ Nevada teachers produced the $90\%$ confidence interval for the mean $\mu$ . The fourth conclusion is: About $9\text{ out of 10}$ teachers surveyed earn between $\$38944\text{ and \$42893}$ . This conclusion is incorrect because the given confidence interval is for the population mean and not for individuals.

(e)

To determine

To explain which conclusion is correct and also what is wrong with others.

Answer to Problem 6E

It is incorrect.

Explanation of Solution

It is given that software analysis of the salaries of a random sample of $288$ Nevada teachers produced the $90\%$ confidence interval for the mean $\mu$ . The fifth conclusion is: We are $90\%$ confident that the average teacher salary in the United States is between $\$38944\text{ and \$42893}$ . This conclusion is incorrect because the sample is only based on Nevada teachers and their salaries could deviate from the salaries of teachers outside of Nevada.