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?
There is a positive association between daylight hours and gym attendance.
The correlation coefficient of r = 0.72 indicates a strong positive relationship between the number of daylight hours and gym attendance, suggesting that as one increases, so does the other.
A negative association would imply that as daylight hours increase, gym attendance decreases, which contradicts the observed correlation coefficient of r = 0.72. A positive value indicates that the two variables move in the same direction, not oppositely.
This choice suggests both a negative relationship and causality, which is inconsistent with the positive correlation found. The correlation indicates that increased daylight hours lead to increased gym attendance, not a decrease, thus making this option incorrect.
This choice accurately reflects the correlation coefficient of r = 0.72, which indicates a strong positive relationship. As daylight hours increase, gym attendance tends to rise, confirming the observed trend.
While there is a positive association, the correlation does not imply causation. Other factors could influence attendance that are not accounted for in the correlation. Therefore, claiming a causal relationship without further evidence is premature.
The correlation coefficient of r = 0.72 signifies a strong positive association between daylight hours and gym attendance, indicating that as daylight increases, attendance tends to increase as well. While this correlation is evident, it does not establish causality, highlighting the importance of cautious interpretation when analyzing relationships in data.
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