Use the Rank Correlation Coefficient to Test for a Correlation

Essay

Use the rank correlation coefficient to test for a correlation between the two variables.
-A placement test is required for students desiring to take a finite mathematics course at a university. The instructor of the course studies the relationship between students' placement test score and final course score. A random sample of eight students yields the following data.

$\begin{array}{ccc}\text { Placement Score }& \text { Final Course Score } \\\hline 38&63\\90&41\\95&54\\51&32\\86&93\\74&60\\60&61\\57&89\end{array}$
Compute the rank correlation coefficient, rs, of the data and test the claim of correlation between placement score and final course score. Use a significance level of 0.05.