Question

I need help with - ​(c)​ 95% of adults in this country worked between 38.7 hours and 44.1 hours last week. - at the bottom - Thank you!

In a​ survey, 1200 adults in a certain country were asked how many hours they worked in the previous week. Based on the​ results, a​ 95% confidence interval for mean number of hours worked was lower​ bound: 38.7 and upper​ bound: 44.1. Which of the following represents a reasonable interpretation of the​ result?

For those that are not​ reasonable, explain the flaw.

(a) There is a​ 95% chance the mean number of hours worked by adults in this country in the previous week was between 38.7 hours and 44.1 hours

A. Flawed. This interpretation implies that the mean is only for last week.

B. Flawed. This interpretation implies that the population mean varies rather than the interval. - (Correct Answer)

C. Correct. This interpretation is reasonable.

D. Flawed. This interpretation makes an implication about individuals rather than the mean. ​

(b) We are​ 95% confident that the mean number of hours worked by adults in this country in the previous week was between 38.7 hours and 44.1 hours.

A. Flawed. This interpretation implies that the population mean varies rather than the interval.

B. Flawed. This interpretation does not make it clear that the​ 95% is the probability that the mean is within the interval.

C. Flawed. This interpretation makes an implication about individuals rather than the mean.

D. Correct. This interpretation is reasonable. - Correct Answer

​(c)​ 95% of adults in this country worked between 38.7 hours and 44.1 hours last week.

A. Flawed. This interpretation implies that the mean is only for last week.

B. Flawed. This interpretation does not make it clear that the​ 95% is the probability that the mean is within the interval.

C. Flawed. This interpretation makes an implication about individuals rather than the mean.

D. Correct. This interpretation is reasonable.

Answer 1

(a) The Interpretation of the confidence interval is flawed. The interpretation implies the population mean varies rather than the interval. It should be stated as, there is 95% chance that the given interval will contain the population mean. Hence, Option (B) is the correct choice. (Ans).

(b) The interpretation about the confidence interval is reasonable. Hence, Option (D) is the correct choice. (Ans).

(c) The interpretation about the confidence interval is flawed. The interpretation makes an implication about individuals rather than the mean. Hence, Option (C) is the correct choice. (Ans).