A student was asked to find a 99% confidence interval for widget width using data from a random sample of size n = 29. Which of the following is a correct interpretation of the interval 14.3 < mu < 30.4? Check all that are correct. A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.
B. The mean width of all widgets is between 14.3 and 30.4,99% of the time. We know this is true because the mean of our sample is between 14.3 and 30.4.
C. There is a 99% chance that the mean of the population is between 14.3 and 30.4.
D. With 99% confidence, the mean width of a randomly selected widget will be between 14.3 and 30.4.
E. There is a 99% chance that the mean of a sample of 29 widgets will be between 14.3 and 30.4.

Using confidence interval concepts, it is found that the correct options are:

A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.

C. There is a 99% chance that the mean of the population is between 14.3 and 30.4.

The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.

In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.

A similar problem is given at link

The correct options are (A), (C) and (D).

Step-by-step 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.

It is provided that the 99% confidence interval for the mean widget width is:

CI = 14.3 < μ < 30.4

The 99% confidence interval for population mean widget width (14.3, 30.4), implies that there is a 0.99 probability that the true value of the mean widget width is included in the above interval.

Or, the 99% confidence interval for the mean widget width implies that there is 99% confidence or certainty that the true mean widget width value is contained in the interval (14.3, 30.4).

Thus, the correct options are (A), (C) and (D).