The following scatterplot shows the percentage of the vote a candidate received in the 2004 senatorial elections according to the voter's income level based on an exit poll of voters conducted by CNN. The income levels 1-8 correspond to the following income classes: 1=Under $15,000; 2=$15-30,000; 3=$30-50,000; 4=$50-75,000; 5=$75-100,000; 6=$100-150,000;
7=$150-200,000; 8=$200,000 or more.
-Use the election scatterplot to the find the value of the rank correlation coefficient $\mathrm { r } _ { \mathrm { s } }$
A) $\mathrm { r } _ { \mathrm { S } } = 0.9762$
B) $\mathrm { r } _ { \mathrm { S } } = 1.9762$
C) $\mathrm { r } _ { \mathrm { S } } = - 1$
D) $\mathrm { r } _ { \mathrm { S } } = - 0.9762$

Question

The following scatterplot shows the percentage of the vote a candidate received in the 2004 senatorial elections according to the voter's income level based on an exit poll of voters conducted by CNN. The income levels 1-8 correspond to the following income classes: 1=Under $15,000; 2=$15-30,000; 3=$30-50,000; 4=$50-75,000; 5=$75-100,000; 6=$100-150,000;
7=$150-200,000; 8=$200,000 or more. 
-Use the election scatterplot to the find the value of the rank correlation coefficient $\mathrm { r } _ { \mathrm { s } }$ 
A) $\mathrm { r } _ { \mathrm { S } } = 0.9762$ 
B) $\mathrm { r } _ { \mathrm { S } } = 1.9762$ 
C) $\mathrm { r } _ { \mathrm { S } } = - 1$ 
D) $\mathrm { r } _ { \mathrm { S } } = - 0.9762$

Quizplus · Accepted Answer

The scatterplot shows a strong negative correlation between income level and percentage of the vote received by the candidate. As income level increases, the percentage of the vote received decreases. Therefore, we can expect a negative rank correlation coefficient. The closest value to the calculated rank correlation coefficient of -0.9762 is choice D, $\mathrm { r } _ { \mathrm { S } } = - 0.9762$.

The Following Scatterplot Shows the Percentage of the Vote a Candidate