The problem asks to determine the correlation coefficient $r$ based on the results of two tests (Tes 1 and Tes 2), and to provide an explanation regarding the outcome.

The data provided is as follows:

$\text{Tes 1:} \quad 15, 14, 10, 9, 8, 8, 7, 6, 2, 2$ $\text{Tes 2:} \quad 4, 3, 4, 8, 7, 8, 10, 9, 14, 14$

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. It can be calculated using the Pearson correlation formula:

[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} ]

Where:

• $x$ represents the values from Tes 1,
• $y$ represents the values from Tes 2,
• $n$ is the number of data points (in this case, 10).

Let me compute the correlation coefficient $r$.The Pearson correlation coefficient $r$ for the two test results is approximately $-0.947$.

Explanation:

This value indicates a strong negative correlation between the two tests. A correlation coefficient of $-1$ would mean a perfect negative linear relationship, while $0$ indicates no linear relationship. Since $r \approx -0.947$, the results suggest that as scores in Tes 1 increase, the scores in Tes 2 tend to decrease in a nearly linear fashion.

Would you like more details on the calculation or interpretation of this result?

Here are some related questions:

1. How does the negative correlation affect interpretations in educational contexts?
2. What other statistical tests can be used to explore relationships between two datasets?
3. Can you explain the steps involved in manually calculating the Pearson correlation coefficient?
4. What are some assumptions behind using the Pearson correlation?
5. How would a positive correlation (e.g., $r = 0.95$) be interpreted in comparison?

Tip: When interpreting correlation coefficients, remember that correlation does not imply causation—other factors may be influencing both datasets.