A Study of the Top 75 MBA Programs Attempted to Predict

question 46

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

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 \(\$ 134,220\).

---

Definitions:

Observed Frequency

The count of occurrences or instances of a particular event or characteristic in a data set.

Chi-squared Distribution

A distribution used in statistics to test hypotheses about the frequency distribution of observed data compared to the expected distribution if the null hypothesis is true.

Alternative Hypothesis

A statement that contradicts the null hypothesis and is considered true if the null hypothesis is rejected based on statistical evidence.

Proportions

Fractions or percentages that represent part of a whole or a ratio of one quantity to another.