A Study of the Top 75 MBA Programs Attempted to Predict

A study of the top 75 MBA programs attempted to predict the average starting salary (in $1000's) of graduates of the program based on the amount of tuition (in $1000's) charged by the program.
The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary
Predictor
$\begin{array} { l r r c l } \text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \\ \text { Constant } & 18.1849 & 10.3336 & 1.76 & 0.0826 \\ \text { Size } & 1.47494 & 0.14017 & 10.52 & 0.0000 \end{array}$

R-Squared $\quad 0.6027 \quad$ Resid. Mean Square (MSE) $532.986$
Adjusted R-Squared $0.5972$ Standard Deviation $\quad 23.0865$

The model was then used to create $95 \%$ confidence and prediction intervals for $y$ and for $\mathrm { E } ( \mathrm { Y } )$ when the tuition charged by the MBA program was $\$ 75,000$ . The results are shown here:
95\% confidence interval for $\mathrm { E } ( \mathrm { Y } )$ : $( \$ 123,390 , \$ 134,220 )$
$95 \%$ prediction interval for $Y$ : $( \$ 82,476 , \$ 175,130 )$
Which of the following interpretations is correct if you want to use the model to estimate $E ( Y )$ for all MBA programs?

A) We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$ .
B) We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$ .
C) We are $95 \%$ confident that the average of all starting salaries for graduates of all MBA programs that charge $\$ 75,000$ in tuition will fall between $\$ 82,476$ and $\$ 175,130$ .
D) We are $95 \%$ confident that the average starting salary for graduates of a single MBA program that charges $\$ 75,000$ in tuition will fall between $\$ 123,390$ and $\$ 134,220$ .

Correct Answer:

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