An Academic Advisor Wants to Predict the Typical Starting Salary $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$

An academic advisor wants to predict the typical starting salary of a graduate at a top business school using the GMAT score of the school as a predictor variable. A simple linear regression of
SALARY versus GMAT using 25 data points is shown below. $$\hat { \beta } _ { 0 } = - 92040 \hat { \beta } 1 = 228 s = 3213 r ^ { 2 } = .66 r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
A $95 \%$ prediction interval for SALARY when GMAT $= 600$ is approximately $( \$ 37,915 , \$ 51,984 )$ . Interpret this interval.

A) We are $95 \%$ confident that the SALARY of a top business school graduate will fall between $\$ 37,915$ and \$51,984.
B) We are $95 \%$ confident that the mean SALARY of all top business school graduates with GMATs of 600 will fall between $\$ 37,915$ and $\$ 51,984$ .
C) We are $95 \%$ confident that the increase in SALARY for a 600 -point increase in GMAT will fall between $\$ 37,915$ and $\$ 51,984$ .
D) We are $95 \%$ confident that the SALARY of a top business school graduate with a GMAT of 600 will fall between $\$ 37,915$ and $\$ 51,984$ .