Use the Spearman Rank Correlation Coefficient to Determine Whether the Correlation

Essay

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is
significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses.
Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and
interpret the decision in the context of the original claim.
-The drama department at a college asked professors and students in the drama department to rank 8 actors
according to their performance. The data are listed below. A 10 is the highest ranking and a 1 the lowest
ranking. Test the claim that there is no correlation between professorsʹ and studentsʹ rankings. Use $$\alpha = 0.05 \text {. }$$ $$\begin{array}{l}\begin{array} { l c c c c c c c c } \hline \text { Actor } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \text { Professors } & 2 & 3 & 6 & 10 & 8 & 1 & 5 & 4\end{array}\\\begin{array} { l l l l l l l l l } \text { Students } && 4 & 3 & 1 & 4 & 5 & 7 & 9 & 6 \\\hline\end{array}\end{array}$$