It just so happens that the average weight of an engineering

It just so happens that the average weight of an engineering student is 185 pounds. Dr. Ogden doesn’t know this, so he decides to randomly sample many engineering students and he gets the following 95% confidence interval: (167.22, 197.30).   What is the probability that his 95% confidence interval captured the true population average?

Solution

The first is to interpret the confidence interval above as stating that 95% of the sample means drawn from the population should fall between 46.90 and 54.10. This is incorrect as the confidence interval concerns the population mean, not the sample means.

The second misconception is to interpret the confidence interval above as stating that there is a 95% probability that the true value of the population mean is between 46.90 and 54.10.

The correct interpretation is that there is a 95% probability that the confidence interval contains the true value of the population mean