Difficulty: Medium

Average Score: 72%

Data was collected on the enrollment in two courses. The resulting correlation coefficient is r = 0.0997. How should this be interpreted?

Rationale

There is a weak positive correlation between the two variables.

A correlation coefficient (r) of 0.0997 indicates a very weak positive relationship between the two variables, suggesting that as one variable increases, the other may also increase slightly, but the relationship is not strong enough to be considered significant.

A (There is a weak positive correlation between the two variables.) CORRECT

This choice accurately reflects the interpretation of the correlation coefficient of 0.0997, as it is close to zero but slightly positive, indicating a minimal tendency for the two variables to increase together.

B (There is a weak negative correlation between the two variables.) YOUR ANSWER

This statement is incorrect because a correlation coefficient close to zero (0.0997) does not indicate a negative relationship. A negative correlation would show a value less than zero, indicating that as one variable increases, the other decreases.

C (There is a strong positive correlation between the two variables.) YOUR ANSWER

This choice misrepresents the correlation coefficient. A strong positive correlation would typically require a value closer to 1.0. With an r value of 0.0997, the relationship is too weak to be classified as strong.

D (There is a strong negative correlation between the two variables.) YOUR ANSWER

This option is incorrect as it suggests a significant negative relationship, which is not supported by the positive value of the correlation coefficient (0.0997). A strong negative correlation would require an r value less than -0.7.

Conclusion

The correlation coefficient of 0.0997 indicates a weak positive correlation between the two variables. While it suggests a slight tendency for one variable to increase as the other does, the relationship is too weak to imply any meaningful connection. Understanding the strength of correlation coefficients is crucial for accurate data interpretation in statistical analysis.

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