Chapter 23, Problem 8E

(a)

To determine

To explain how should viewers interpret this news and comment on each of these statements.

Answer to Problem 8E

It is incorrect.

Explanation of Solution

It is given that based on the meteorological data for the past century, a local TV weather forecast estimates that the region’s average winter rainfall is $23\text{'}\text{'}$ , with margin of error of $\pm 2$ inches. They have assumed that he has used a $95\%$ confidence interval. Thus, the first interpretation is: During $95\text{ of the last 100}$ winters, the region got between $21\text{'}\text{'}\text{ and 25''}$ of now. This interpretation is incorrect because the given confidence interval is for the population mean and not for individual winters.

(b)

To determine

To explain how should viewers interpret this news and comment on each of these statements.

Answer to Problem 8E

It is incorrect.

Explanation of Solution

It is given that based on the meteorological data for the past century, a local TV weather forecast estimates that the region’s average winter rainfall is $23\text{'}\text{'}$ , with margin of error of $\pm 2$ inches. They have assumed that he has used a $95\%$ confidence interval. Thus, the second interpretation is: There is a $95\%$ chance the region will get between $21\text{'}\text{'}\text{ and 25''}$ of snow this winter. This interpretation is incorrect because the given confidence interval is for the population mean and not for individual winters.

(c)

To determine

To explain how should viewers interpret this news and comment on each of these statements.

Answer to Problem 8E

It is incorrect.

Explanation of Solution

It is given that based on the meteorological data for the past century, a local TV weather forecast estimates that the region’s average winter rainfall is $23\text{'}\text{'}$ , with margin of error of $\pm 2$ inches. They have assumed that he has used a $95\%$ confidence interval. Thus, the third interpretation is:There will be between $21\text{'}\text{'}\text{ and 25''}$ of snow on the ground for $95\%$ of the winter days. This interpretation is incorrect because the given confidence interval is for the population mean and not for individual winter days.

(d)

To determine

To explain how should viewers interpret this news and comment on each of these statements.

Answer to Problem 8E

It is correct.

Explanation of Solution

It is given that based on the meteorological data for the past century, a local TV weather forecast estimates that the region’s average winter rainfall is $23\text{'}\text{'}$ , with margin of error of $\pm 2$ inches. They have assumed that he has used a $95\%$ confidence interval. Thus, the fourth interpretation is: Residents can be $95\%$ sure that the area’s average snowfall is between $21\text{'}\text{'}\text{ and 25''}$ . This interpretation is correct because $95\%$ of all possible sample will have a confidence interval that contains the population mean if the confidence level of the confidence interval is $95\%$ .

(e)

To determine

To explain how should viewers interpret this news and comment on each of these statements.

Answer to Problem 8E

It is incorrect.

Explanation of Solution

It is given that based on the meteorological data for the past century, a local TV weather forecast estimates that the region’s average winter rainfall is $23\text{'}\text{'}$ , with margin of error of $\pm 2$ inches. They have assumed that he has used a $95\%$ confidence interval. Thus, the fifth interpretation is:Residents can be $95\%$ confident that the average snowfall during the last century was between $21\text{'}\text{'}\text{ and 25''}$ per winter. This interpretation is incorrect because residents can be $100\%$ confident that the average snowfall during the last century was between $21\text{'}\text{'}\text{ and 25''}$ per winter, since we know that the region’s average winter snowfall during the last century was $23\text{'}\text{'}$ .