Use the Rank Correlation Coefficient to Test for a Correlation

question 21

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 $\alpha = 0.05$ .

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Definitions:

Family Roles

The specific functions, duties, and expectations assigned to each member within a family structure, influencing their behavior and interactions.

Conflicts Associated

This refers to the disputes, disagreements, or tensions that are connected with or arise in relation to a specific issue, situation, or context.

Roles

The functions, behaviors, and responsibilities expected of individuals within specific social positions or contexts.

Worldview Differences

Variances in the fundamental cognitive orientations of individuals or groups, including their beliefs about the nature of reality, values, and ethics.