A company is considering recruiting new employees from a particular college and plans to place a great deal of emphasis on the student’s college GPA. However, the company is aware that not all schools have the same grading standards, so it is possible that a student at this school might have a lower (or higher) GPA than a student from another school, yet really be on par with the other student. To make this comparison between schools, the company has devised a test that it has administered utilizing a sample size of 400 students. With the results of the test, it has developed a regression model that it uses to predict student GPA. The following equation represents the model:

The R2 for this model is 0.88 and the standard error of the estimate is 0.20, based on the sample data used to develop the model. Note that the dependent variable is the GPA and the independent variable is test score, where this score can range from 0 to 100. For the sample data used to develop the model, the following values are known:

a. Based on the information contained in this problem, can you conclude that as the test score increases, the GPA will also increase, using a significance level of 0.05?
b. Suppose a student interviews with this company, takes the company test, and scores 80 correct. What is the 90% prediction interval estimate for this student’s GPA? Interpret the interval.
c. Suppose the student in part b actually has a 2.90 GPA at this school. Based on this evidence, what might be concluded about this person’s actual GPA compared with other students with the same GPA at other schools? Discuss the limitations you might place on this conclusion.
d. Suppose a second student with a 2.45 GPA took the test and scored 65 correct. What is the 90% prediction interval for this student’s “real” GPA? Interpret.