The article “First Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students” (Journal of College Student Development [1999]: 599–610) reported that the sample mean and standard deviation for high school grade point average (GPA) for students enrolled at a large research university were 3.73 and 0.45, respectively. Suppose that the mean and standard deviation were based on a random sample of 900 students at the university.

a. Construct a 95% confidence interval for the mean high school GPA for students at this university.

b. Suppose that you wanted to make a statement about the range of GPAs for students at this university. Is it reasonable to say that 95% of the students at the university have GPAs in the interval you computed in Part (a)? Explain.