Question 3

A high school guidance counselor collected the following data about the grade point average (GPA) and the SAT mathematics test score for 6 graduating students.

GPA 2.7 3.5 3.7 3.3 3.6 3.0 SAT 450 570 700 620 640 580

(a) Calculatethesamplecorrelationcoefficientforthisdata.

(b) ExplainwhatthecorrelationcoefficientsaysabouttherelationshipbetweenGPAandSATscores? (c) What does it mean for two variables to be independent? Are SAT and GPA independent?

(d) Is the sample correlation coefficient a random variable? Does it have a sampling distribution?