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 college administrator collected information on first-semester night-school students. A random sample taken of 12 students yielded the following data on age and GPA during the first semester.
$\begin{array}{llcc} \text { Age} & \text { GPA} \\ \underline{\text {x }} & \underline{\text {y}}\\18&1.2\\26&3.8\\27&2.0\\37&3.3\\33&2.5\\47&1.6\\20&1.4\\48&3.6\\50&3.7\\38&3.4\\34&2.7\\22&2.8\end{array}$
Do the data provide sufficient evidence to conclude that the variables age, $x$ , and GPA, $y$ , are correlated? Apply a rank-correlation test. Use $\alpha = 0.05$ .