Find the Critical Value $\mathrm { r } _ { \mathrm { S } }$

Essay

Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data.
-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.
Compute the rank correlation coefficient, $\mathrm { r } _ { \mathrm { S } }$ of the data and test the claim of correlation between placement score and final course score. Use a significance level of $0.05$ .