A Study of the Top MBA Programs Attempted to Predict $95 \%$

Multiple Choice

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs) of graduates of the program based on the amount of tuition (in $1000ʹs) charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below: Least Squares Linear Regression of Salary
Predictor


The model was then used to create $95 \%$ confidence and prediction intervals for $y$ and for $E ( Y )$ when the tuition charged by the MBA program was $\$ 75,000$ and the GMAT score was 675 . The results are shown here:
$95 \%$ confidence interval for $\mathrm { E } ( \mathrm { Y } )$ : $( \$ 126,610 , \$ 136,640 )$
$95 \%$ prediction interval for $Y$ : $( \$ 90,113 , \$ 173,160 )$
Which of the following interpretations is correct if you want to use the model to estimate $Y$ for a single MBA program?

A) We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition and has an average GMAT score of 675 will fall between $\$ 126,610$ and $\$ 136,640$ .
B) We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition and has an average GMAT score of 675 will fall between $\$ 90,113$ and $\$ 173,16,30$ .
C) We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition and have an average GMAT score of 675 will fall between $\$ 90,113$ and $\$ 173,16,30$ .
D) We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition and have an average GMAT score of 675 will fall between $\$ 126,610$ and $\$ 136,640$ .