Part of a university's professor's job is to publish his or her research. this task often entails reading a variety of journal articles to keep up to date. to determine faculty standards, a dean of a business school surveyed a random sample of 12 professors across the country and asked them to count the number of journal articles they read in a typical month. these data are listed here. estimate with 90% confidence the mean number of journal articles read monthly by professors.9 17 4 23 56 30 41 45 21 10 44 20

(18.1042, 35.2292) is a 90% confidence interval for the mean number of journal articles read monthly by professors.

Step-by-step explanation:

We have a small sample of size n = 12, and s = 16.5163. A pivotal quantity for this case is given by which has a t distribution with n-1 degrees of freedom if we suppose that we take the sample from the normal population. The confidence interval is given by where is the th quantile of the t distribution with n - 1 = 12 - 1 = 11 degrees of freedom. As we want the 90% confidence interval, we have that and the confidence interval is where is the 5th quantile of the t distribution with 11 df, i.e., . Then, we have and the 90% confidence interval is given by (18.1042, 35.2292).