Two NFL scouts are in the process of recruiting 7 college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.The rankings are given below. $$\begin{array} { c c c }
\begin{array} { c }
\text { Player } \
\text { (Receiver) }
\end{array} & \begin{array} { c }
\text { Rankings of } \
\text { Scout } 1
\end{array} & \begin{array} { c }
\text { Rankings of } \
\text { Scout } 2
\end{array} \
1 & 3 & 3 \
2 & 2 & 1 \
3 & 1 & 2 \
4 & 4 & 6 \
5 & 5 & 4 \
6 & 7 & 7 \
7 & 6 & 5
\end{array}$$
At ? = .05,does it appear that the two scouts have similar opinions about the professional football career prospects of the seven players?
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$\begin{array} { c c c c c }
\text { Receiver } & \text { Rankings of } & \text { Rcoutkings of } & d _ { i } & d _ { i } ^ { 2 } \
1 & 3 & \text { Scout } 2 & 3 & 0 \
2 & 2 & 1 & 1 & 1 \
3 & 1 & 2 & - 1 & 1 \
4 & 4 & 6 & - 2 & 4 \
5 & 5 & 4 & 1 & 1 \
6 & 7 & 7 & 0 & 0 \
7 & 6 & 5 & 1 & 1 \
& & & \text { Total } = & 8
\end{array}$$
$$\begin{array} { l }
\sum d _ { i } ^ { 2 } = 8 \
r _ { s } = 1 - \frac { 6 \sum d _ { i } ^ { 2 } } { n \left( n ^ { 2 } - 1 \right) } = 1 - \left[ \frac { ( 6 ) ( 8 ) } { 7 \left( 7 ^ { 2 } - 1 \right) } \right] = 1 - .1429 = .8571
\end{array}$$

Question

Two NFL scouts are in the process of recruiting 7 college senior football players (receivers).After a careful review and evaluation,both scouts ranked the seven receivers in terms of their professional career prospects.The rankings are given below. $$\begin{array} { c c c } 
\begin{array} { c } 
\text { Player } \
\text { (Receiver) }
\end{array} & \begin{array} { c } 
\text { Rankings of } \
\text { Scout } 1
\end{array} & \begin{array} { c } 
\text { Rankings of } \
\text { Scout } 2
\end{array} \
1 & 3 & 3 \
2 & 2 & 1 \
3 & 1 & 2 \
4 & 4 & 6 \
5 & 5 & 4 \
6 & 7 & 7 \
7 & 6 & 5
\end{array}$$
At ? = .05,does it appear that the two scouts have similar opinions about the professional football career prospects of the seven players?
A)Reject the null hypothesis.
B)Do not reject the null hypothesis.
$$\begin{array} { c c c c c } 
\text { Receiver } & \text { Rankings of } & \text { Rcoutkings of } & d _ { i } & d _ { i } ^ { 2 } \
1 & 3 & \text { Scout } 2 & 3 & 0 \
2 & 2 & 1 & 1 & 1 \
3 & 1 & 2 & - 1 & 1 \
4 & 4 & 6 & - 2 & 4 \
5 & 5 & 4 & 1 & 1 \
6 & 7 & 7 & 0 & 0 \
7 & 6 & 5 & 1 & 1 \
& & & \text { Total } = & 8
\end{array}$$
$$\begin{array} { l } 
\sum d _ { i } ^ { 2 } = 8 \
r _ { s } = 1 - \frac { 6 \sum d _ { i } ^ { 2 } } { n \left( n ^ { 2 } - 1 \right) } = 1 - \left[ \frac { ( 6 ) ( 8 ) } { 7 \left( 7 ^ { 2 } - 1 \right) } \right] = 1 - .1429 = .8571
\end{array}$$

Quizplus · Accepted Answer

We need to test if the rankings given by the two scouts are significantly different or not. For that, we use the Spearman's rank correlation coefficient (rs). The null hypothesis is that the two ranks are not significantly different, and the alternative hypothesis is that they are significantly different. At α = .05, the critical value for rs with n=7 is ±0.684. The calculated value of rs is 0.8571, which is greater than the critical value. Therefore, we reject the null hypothesis and conclude that the two scouts have significantly different opinions about the professional football career prospects of the seven players.

Two NFL Scouts Are in the Process of Recruiting 7