In Order for Applicants to Work for the Foreign-Service Department $\alpha$

Essay

In order for applicants to work for the foreign-service department, they must take a test in the language of the
country where they plan to work. The data below shows the relationship between the number of years that
applicants have studied a particular language and the grades they received on the proficiency exam. Test the
significance of the correlation coefficient using α $\alpha$ = 0.10 and the claim ρ $\varrho = 0$ $$\begin{array} { l | c | c | c | c | c | c | c | c | c | } \text { Number of years, } \mathrm { x } & 2 & 3 & 3 & 4 & 2 & 5 & 1 & 6 & 2 \\\hline \text { Grades on test, } \mathrm { y } & 58 & 65 & 72 & 79 & 70 & 87 & 55 & 90 & 69\end{array}$$