Chapter 23, Problem 7E

(a)

To determine

To comment on the following interpretation.

Explanation of Solution

After surveying students at Dartmouth College, a campus organization calculated that a $95\%$ confidence interval for the mean cost of food for one term is $(\$1102,\$1290)$ . Now the organization wants to write a report and is considering the interpretations. Thus, we have first interpretation as: $95\%$ of all students pay between $(\$1102,\$1290)$ for food. This interpretation is incorrect because the given confidence interval is for the population mean and not for individuals.

(b)

To determine

To comment on the following interpretation.

Explanation of Solution

After surveying students at Dartmouth College, a campus organization calculated that a $95\%$ confidence interval for the mean cost of food for one term is $(\$1102,\$1290)$ . Now the organization wants to write a report and is considering the interpretations. Thus, we have second interpretation as: $95\%$ of the sampled students paid between $(\$1102,\$1290)$ . This interpretation is incorrect because the given confidence interval is for the population mean and not for individuals.

(c)

To determine

To comment on the following interpretation.

Explanation of Solution

After surveying students at Dartmouth College, a campus organization calculated that a $95\%$ confidence interval for the mean cost of food for one term is $(\$1102,\$1290)$ . Now the organization wants to write a report and is considering the interpretations. Thus, we have second interpretation as: We are $95\%$ sure that the students in this sample averaged between $(\$1102,\$1290)$ for food. We can say about this interpretation that we are $100\%$ sure that the average salary in this sample was between $(\$1102,\$1290)$ , since the average salary in this sample is $\$1196$ .

(d)

To determine

To comment on the following interpretation.

Explanation of Solution

After surveying students at Dartmouth College, a campus organization calculated that a $95\%$ confidence interval for the mean cost of food for one term is $(\$1102,\$1290)$ . Now the organization wants to write a report and is considering the interpretations. Thus, we have second interpretation as: $95\%$ of all samples of students will have average food costs between $(\$1102,\$1290)$ . This interpretation is incorrect because the confidence interval is about the population mean and not the sample mean of other samples.

(e)

To determine

To comment on the following interpretation.

Explanation of Solution

After surveying students at Dartmouth College, a campus organization calculated that a $95\%$ confidence interval for the mean cost of food for one term is $(\$1102,\$1290)$ . Now the organization wants to write a report and is considering the interpretations. Thus, we have second interpretation as: We are $95\%$ sure that the average amount all students pay is between $(\$1102,\$1290)$ . This interpretation is correct because $95\%$ of all possible sample will have a confidence interval that contains the population mean.