Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
$\begin{array}{lll}
& \underline{\text { PhDs}}& \underline{\text { Mules }}\
\text { Mean } & 40 & 200 \
\text { Standard Deviation } & 15 & 50
\end{array}$
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.
-Look at Data Set 6-1. For a state with no PhDs the predicted number of mules is
A) 320
B) 80
C) 20
D) none of the other alternatives are correct.

Question

Data Set 6-1
The correlation between the number of PhDs and the number of mules in a state used to be approximately -.90. Accept the following simplified summary data.
 $\begin{array}{lll}
& \underline{\text { PhDs}}& \underline{\text { Mules }}\
\text { Mean } & 40 & 200 \
\text { Standard Deviation } & 15 & 50
\end{array}$ 
In questions based on Data Set 6-1, the task is to predict the number of mules for a state, given the number of PhDs.
-Look at Data Set 6-1. For a state with no PhDs the predicted number of mules is
A) 320
B) 80
C) 20
D) none of the other alternatives are correct.

Quizplus · Accepted Answer

The prediction equation for a linear relationship can be represented as $y = mx + b$, where $m$ is the slope, $x$ is the independent variable (number of PhDs in this case), and $b$ is the y-intercept. Given the negative correlation of approximately -0.90, as the number of PhDs decreases to 0, the number of mules would increase. The y-intercept in this context represents the predicted number of mules when the number of PhDs is 0. Since we are not provided with the exact regression equation, we cannot calculate the exact number directly from the given statistics. However, the correct answer must logically be higher than the mean number of mules (200) due to the strong negative correlation. Therefore, the only option that fits this description is 320 mules, making A the correct choice by elimination and understanding of the relationship between the variables.

Data Set 6-1 the Correlation Between the Number of PhDs

Data Set 6-1
the Correlation Between the Number of PhDs