43. Data was collected on the enrollment in two courses. The resulting correlation coefficient is r = 0.0997. How should this be interpreted?
Answer: A
There is a weak positive correlation between the two variables.
The correlation coefficient of r = 0.0997 indicates a weak positive relationship between the enrollment in the two courses, suggesting that as one variable increases, the other tends to increase slightly as well.
A) There is a weak positive correlation between the two variables.
This option accurately reflects the interpretation of the correlation coefficient of r = 0.0997, as values of r between 0 and 0.3 indicate a weak positive correlation. This means that there is a slight tendency for increases in one variable to be associated with increases in the other.
B) There is a weak negative correlation between the two variables.
This option is incorrect because a negative correlation would be indicated by a correlation coefficient less than zero. Since r = 0.0997 is positive, it does not support the notion of a negative relationship.
C) There is a strong positive correlation between the two variables.
This option is incorrect as a strong positive correlation would require a correlation coefficient closer to 1. A value of r = 0.0997 indicates only a weak positive relationship, not a strong one.
D) There is a strong negative correlation between the two variables.
This option is incorrect because a strong negative correlation would require a correlation coefficient significantly less than zero. The positive value of r = 0.0997 indicates the absence of a negative relationship.
Conclusion
The correct interpretation of the correlation coefficient r = 0.0997 is that there is a weak positive correlation between the two variables, which is supported by the definition of correlation strength. All other options misinterpret the correlation coefficient, either suggesting a negative relationship or overestimating the strength of the positive relationship.