Choose the one alternative that best completes the statement or answers the question.
-The history department at a college asked its professors and students to rank 8 guest speakers according to their communication skills. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Find the test statistic to test the hypothesis of no correlation between the rankings. Use
$$\alpha = 0.05 \text {. }$$
$\begin{array}{lcccccccc}
\hline \text { Speaker } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline \text { Professors } & 2 & 3 & 6 & 10 & 8 & 1 & 5 & 4 \
\text { Students } & 4 & 3 & 1 & 4 & 5 & 7 & 9 & 6
\end{array}$

A) $- 0.208$
B) $- 0.198$
C) $- 0.354$
D) $- 0.278$

Question

Choose the one alternative that best completes the statement or answers the question.
-The history department at a college asked its professors and students to rank 8 guest speakers according to their communication skills. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Find the test statistic to test the hypothesis of no correlation between the rankings. Use
$$\alpha = 0.05 \text {. }$$
$\begin{array}{lcccccccc}
\hline \text { Speaker } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \
\hline \text { Professors } & 2 & 3 & 6 & 10 & 8 & 1 & 5 & 4 \
\text { Students } & 4 & 3 & 1 & 4 & 5 & 7 & 9 & 6
\end{array}$

A) $- 0.208$
B) $- 0.198$
C) $- 0.354$
D) $- 0.278$

Quizplus · Accepted Answer

The correct answer is A. The test statistic for the hypothesis of no correlation between the rankings is -0.208. This is calculated using the formula:$$r_s = 1 - \frac{6\sum d^2}{n(n^2-1)}$$where $r_s$ is the Spearman's rank correlation coefficient, $d$ is the difference between the ranks of the two variables, and $n$ is the number of observations. In this case, $n = 8$, and the differences between the ranks are:$$d_1 = 2, d_2 = 0, d_3 = -5, d_4 = 6, d_5 = 3, d_6 = -6, d_7 = 4, d_8 = -2$$Plugging these values into the formula, we get:$$r_s = 1 - \frac{6(2^2 + 0^2 + (-5)^2 + 6^2 + 3^2 + (-6)^2 + 4^2 + (-2)^2)}{8(8^2-1)}$$$$r_s = 1 - \frac{6(42)}{8(63)}$$$$r_s = 1 - 0.208$$$$r_s = -0.208$$

Choose the One Alternative That Best Completes the Statement or Answers