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A Study of the Top 75 MBA Programs Attempted to Predict

question 106

Multiple Choice

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
$\begin{array} { l r c c l } \text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \\ \text { Constant } & 18.1849 & 10.3336 & 1.76 & 0.0826 \\ \text { Size } & 1.47494 & 0.14017 & 10.52 & 0.0000 \end{array}$

$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 $1000's) charged by the program. The results of a simple linear regression analysis are shown below: Least Squares Linear Regression of Salary Predictor \begin{array} { l r c c l } \text { Variables } & \text { Coefficient } & \text { Std Error } & \text { T } & \text { P } \\ \text { Constant } & 18.1849 & 10.3336 & 1.76 & 0.0826 \\ \text { Size } & 1.47494 & 0.14017 & 10.52 & 0.0000 \end{array} The model was then used to create 95 \% confidence and prediction intervals for y and for E ( Y ) when the tuition charged by the MBA program was \$ 75,000 . The results are shown here: 95\% confidence interval for \mathrm { E } ( \mathrm { Y } ) : ( \$ 123,390 , \$ 134,220 ) 95 \% prediction interval for Y : ( \$ 82,476 , \$ 175,130 ) Which of the following interpretations is correct if you want to use the model to predict Y for a single MBA programs? A) We are 95 \% confident that the average of all starting salaries for graduates of all MBA programs that charge \$ 75,000 in tuition will fall between \$ 82,476 and \$ 175,130 . B) We are 95 \% confident that the average starting salary for graduates of a single MBA program that charges \$ 75,000 in tuition will fall between \$ 82,476 and \$ 175,130 . C) We are 95 \% confident that the average starting salary for graduates of a single MBA program that charges \$ 75,000 in tuition will fall between \$ 123,390 and \$ 134,220 . D) We are 95 \% confident that the average of all starting salaries for graduates of all MBA programs that charge \$ 75,000 in tuition will fall between \$ 123,390 and \$ 134,220 .$

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 $\$ 75,000$ . 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 predict $Y$ for a single MBA programs?

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