6. A fitness center owner notices that gym attendance increases as the number of daylight hours increases. The owner calculates a correlation coefficient between daylight hours and gym attendance of r = 0.72. Based on this information, what can be concluded?
Answer: C
There is a positive association between daylight hours and gym attendance.
The correlation coefficient of r = 0.72 indicates a strong positive association between the number of daylight hours and gym attendance. This suggests that as daylight hours increase, gym attendance also tends to increase.
A) There is a negative association between daylight hours and gym attendance.
This option is incorrect because the correlation coefficient of r = 0.72 reflects a positive relationship, not a negative one. A negative association would mean that as one variable increases, the other decreases, which contradicts the provided data.
B) There is a negative, causal relationship between daylight hours and gym attendance.
This option is also incorrect. Not only does the correlation coefficient indicate a strong positive relationship, but it also does not support the claim of a negative relationship. Moreover, causation cannot be established solely based on correlation; thus, this option is unfounded.
C) There is a positive association between daylight hours and gym attendance.
This statement is correct, as evidenced by the positive correlation coefficient of r = 0.72. This indicates that as daylight hours increase, gym attendance also tends to increase, confirming a positive association.
D) There is a positive, causal relationship between daylight hours and gym attendance.
While this option correctly identifies the positive nature of the relationship, it incorrectly suggests causation. Correlation does not imply causation; therefore, it cannot be concluded that increased daylight hours cause an increase in gym attendance based solely on the correlation coefficient.
Conclusion
The correct answer, C, accurately reflects the observed strong positive association indicated by the correlation coefficient. Options A and B misinterpret the nature of the relationship by stating it is negative, while D oversteps by asserting a causal link that cannot be confirmed through correlation alone. Thus, C stands out as the only appropriate conclusion based on the data provided.