Question

In a​ survey, 13001300 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: 39.639.6 and upper​ bound: 43.943.9. 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 39.639.6 hours and 43.943.9 hours. A. Flawed. This interpretation implies that the population mean varies rather than the interval. B. Flawed. This interpretation implies that the mean is only for last week. C. Flawed. This interpretation makes an implication about individuals rather than the mean. D. Correct

Answer 1

The correct option is (A).

Explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for mean number of hours worked was,

CI = (39.6 hours, 43.9 hours).

The 95% confidence interval for mean number of working hours, (39.6, 43.9) hours, implies that the true mean number of working hours for the adults of the country lies in this interval with probability 0.95.

So, there is a 95% confidence or chance that the true mean values lies in the interval (39.6, 43.9).

Thus, the correct option is (A).