A study of 31 college graduates from Northern California colleges and universities looked at the Math SAT score for each student and the student's GPA in the STEM courses they took at their college or university. The following summary statistics were recorded X = 550, y = 2.95, Sx = 38.7 Sy = 0.28, r = 0.56 where xj = Math SAT score of the jth student and y; = GPA in college STEM courses of the jth student. (a) Is the sample correlation between Math SAT scores and College STEM GPAs significant? Justify your answer with a hypothesis test, and show your work.
(b) What percentage of the variation in STEM GPAs is explained by Math SAT scores? Explain briefly how you found your answer.
(c) Find the regression equation that predicts College STEM GPA from Math SAT score. Show your work.
(d) Ronny scored 620 on the Math SAT. What is their predicted STEM GPA at Cal State East Bay? Include a margin of error, and state the assumption(s) (if any) that justify its use. As always – show all your work.