Question

A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 21. Which of the following is a correct interpretation of the interval 10.6 < μ < 29.1? Check all that are correct.

A. With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
B. With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
C. The mean width of all widgets is between 10.6 and 29.1, 95% of the time.
D. We know this is true because the mean of our sample is between 10.6 and 29.1.
E. There is a 95% chance that the mean of the population is between 10.6 and 29.1.
F. There is a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.

Answer 1

Explanation:

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.

With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is

With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.