a study reports that college students work, on average, between 4.63 and 12.63 hours a week, with confidence coefficient .95. which of the following statements are correct?

MARK ALL THAT ARE TRUE. There are four correct answers. (MARK ALL)

A. The interval was produced by a technique that captures mu 95% of the time.

B. 95% of all college students work between between 4.63 and 12.63 hours a week.

C. 95% of all samples will have x-bar between between 4.63 and 12.63.

D. The probability that mu is between 4.63 and 12.63 is .95.

E. 95% of samples will produce intervals that contain mu.

F. The probability that mu is included in a 95% CI is .95.

G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week.

I’m not so sure. See –

A. The interval was produced by a technique that captures mu 95% of the time. TRUE – That is what “95% confidence” means.

B. 95% of all college students work between between 4.63 and 12.63 hours a week.

C. 95% of all samples will have x-bar between between 4.63 and 12.63.

D. The probability that mu is between 4.63 and 12.63 is .95. FALSE – The population mean will be between the end points of the interval for 95% of all samples. But since each sample will have a different mean, the end points of those intervals will also change. This interval either includes m, or it doesn’t. Once I take a sample and compute x-bar, there is no more probability involved.

E. 95% of samples will produce intervals that contain mu.

F. The probability that mu is included in a 95% CI is .95. TRUE – As long as we talk about the probability of AN interval, not THIS interval.

G. We are 95% confident that the population mean time that college students work is between 4.63 and 12.63 hours a week. TRUE: We are trying to estimate the population mean.

Source: Wikipedia