Chapter 3, Problem 7QAP

Suppose that for a recent admissions class, an Ivy League college received 2,851 applications for early admission. Of this group, it admitted 1,033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. Use the data to estimate P(E), P(R), and P(D). Are events E and D mutually exclusive? Find . For the 2,375 students who were admitted, what is the probability that a randomly selected student was accepted during early admission? Suppose a student applies for early admission. What is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?

The Scholastic Aptitude Test (or SAT) is a standardized college entrance test that is used by colleges and universities as a means for making admission decisions. The critical reading and mathematics components of the SAT are reported on a scale from 200 to 800. Several universities believe these scores are strong predictors of an incoming student’s potential success, and they use these scores as important inputs when making admission decisions on potential freshman. The tile RugglesCollege contains freshman year GPA and the critical reading and mathematics SAT scores for a random sample of 200 students who recently completed their freshman year at Ruggles College. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores as independent variables. How much variation in freshman GPA is explained by this model? Test whether each of the regression parameters β0, β1, and β2, is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable? Using the multiple linear regression model you developed in part (a), what is the predicted freshman GPA of Bobby Engle, a student who has been admitted to Ruggles College with a 660 SAT score on critical reading and at a 630 SAT score on mathematics? The Ruggles College Director of Admissions believes that the relationship between a student’s scores on the critical reading component of the SAT and the student’s freshman GPA varies with the student’s score on the mathematics component of the SAT. Develop an estimated multiple regression equation that includes critical reading and mathematics SAT scores and their interaction as independent variables. How much variation in freshman GPA is explained by this model? Test whether each of the regression parameters β0, β1, β2, and β3 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Do these results support the conjecture made by the Ruggles College Director of Admissions? Do you prefer the estimated regression model developed in part (a) or part (c)? Explain. What other factors could be included in the model as independent variables?

Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job, his goal is to become an investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University or Mount Perry College. Although internships are encouraged by both schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will allow its students to work while enrolled in its MBA program. Ben currently works at the money management firm of Dewey and Louis. His annual salary at the firm is $65,000 per year, and his salary is expected to increase at 3 percent per year until retirement. He is currently 28 years old and expects to work for 40 more years. His current job includes a fully paid health insurance plan, and his current average tax rate is 26 percent. Ben has a savings account with enough money to cover the…