Suppose the correlation coefficient between the number of professional sports teams in a city and the number of hospitals is 0.72. Which statement must be true?A.As the number of sports teams increases, the number of hospitals tends to increase.B.Having more sports teams causes the number of hospitals to increase because athletes often get injured.C.As the number of sports teams increases, the number of hospitals tends to decrease.D.Having more hospitals causes the number of sports teams to increase because teams need to be close to good medical care.
Question
Suppose the correlation coefficient between the number of professional sports teams in a city and the number of hospitals is 0.72. Which statement must be true?A.As the number of sports teams increases, the number of hospitals tends to increase.B.Having more sports teams causes the number of hospitals to increase because athletes often get injured.C.As the number of sports teams increases, the number of hospitals tends to decrease.D.Having more hospitals causes the number of sports teams to increase because teams need to be close to good medical care.
Solution
The statement that must be true is A. As the number of sports teams increases, the number of hospitals tends to increase. This is because a correlation coefficient of 0.72 indicates a strong positive relationship between the two variables. However, it's important to note that correlation does not imply causation, so we cannot say that having more sports teams causes the number of hospitals to increase (option B), or vice versa (option D). Option C is incorrect because a positive correlation means that as one variable increases, the other tends to increase as well, not decrease.
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