In a survey 600 adults in a certain country were asked how m

In a survey, 600 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: 39.9 and upper bound: 44.6. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw.

(b). We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 39.9 hours and 44.6 hours.

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

B. Correct

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

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

(c.) 95% of adults in this country worked between 39.9 hours and 44.6 hours last week.

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

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

C. Correct

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

(d) We are 95% confident that the mean number of hours worked by adults in a particular area of this country in the previous week was between 39.9 hours and 44.6 hours.

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

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

C. Flawed. The interpretation should be about the mean number of hours worked by adults in the whole family, not about in the particular area.

D Correct

Solution

The answer is B. The interpretation is correct.

We can also interpret as

the probability that mean  number of hours worked by adults in this country in the previous week was between 39.9 hours and 44.6 hours is 0.95