Use the Rank Correlation Coefficient to Test for a Correlation

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. $$\begin{array} { | c c | } \hline \text { Placement Score } & \text { Final Course Score } \\& 63 \\90 & 41 \\95 & 54 \\51 & 32 \\86 & 93 \\74 & 60 \\60 & 61 \\57 & 89\end{array}$$ 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.