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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?

Definitions:

Irrelevant Detail

Information that does not have a direct impact on the conclusion or outcome of a particular issue or situation.

Ceteris Paribus

A Latin term meaning "all other things being equal," used to isolate the effect of one variable in a economic model.

Variables

Elements, features, or factors that are liable to vary or change, often used in mathematical models or experiments to calculate outcomes or effects.

Positive Statement

An objective statement based on factual evidence that can be tested and validated as true or false.