The Dean of the Business School at a Small Florida $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$

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 results of the simple linear regression are provided below.
$$\begin{array} { l l } \hat{y} = 4.25 + 2.75 x , \quad & S S x y = 5.15 , S S x x = 1.87 \\& S S y y = 15.17 , S S E = 1.0075 \\\text { Range of the } x \text {-values: } & 2.23 - 3.85 \\\text { Range of the } y \text {-values: } & 9.3 - 15.6\end{array}$$ Suppose a 95% prediction interval for y when x = 3.00 is (16, 21) . Interpret the interval.

A) We are 95% confident that the starting salary of a Business School graduate with a GPA of 3.00 will fall between $16,000 and $21,000.
B) We are 95% confident that the mean starting salary of all Business School graduates with GPAs of 3.00 will fall between $16,000 and $21,000.
C) We are 95% confident that the starting salary of a Business School graduate will increase between $16,000 and $21,000 for every 3-point increase in GPA.
D) We are 95% confident that the starting salary of a Business School graduate will fall between $16,000 and $21,000.