Question

"The scores X on a pretest for a college statistics course and the course grade Y were recorded for 10 students. The results are as follows: X ---- 75,81, 57, 79, 68, 93, 96, 84, 41, 89 Y ----- 2, 3, 1, 2, 1, 4, 4, 3, 1, 3 What might you conclude?"

A. There is absolutely no correlation between the scores and grades
given.
B. There is a very weak correlation between the scores and grades given.
C. There is a moderate correlation between the scores and grades.
D. There is a strong correlation between the scores and grades.

Answer 1

Explanation:

C. There is a moderate correlation between the scores and grades.

Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.

The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.

In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.

However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.