The Dean of the Business School at a Small Florida $( x )$

Multiple Choice

The dean of the Business School at a small Florida college wishes to determine whether the grade-point average (GPA) of a graduating student can be used to predict the graduate's starting salary. More specifically, the dean wants to know whether higher GPAs lead to higher starting salaries. Records for 23 of last year's Business School graduates are selected at random, and data on GPA $( x )$ and starting salary $( y$ , in \$thousands) for each graduate were used to fit the model
$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x .$$
The value of the test statistic for testing $\beta _ { 1 }$ is 17.169. Select the proper conclusion.

A) There is sufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary.
B) There is insufficient evidence (at $\alpha = .10$ ) to conclude that GPA is a useful linear predictor of starting salary.
C) There is insufficient evidence (at $\alpha = .05$ ) to conclude that GPA is positively linearly related to starting salary.
D) At any reasonable $\alpha$ , there is no relationship between GPA and starting salary.