Difficulty: Hard

Average Score: 49%

Which of the following statements demonstrates a negative correlation between two variables?

Rationale

Tennis balls that are older tend to have less bounce.

A negative correlation between two variables means that as one variable increases, the other decreases. This is demonstrated by the statement that older tennis balls have less bounce, implying that as the age of the tennis ball (variable one) increases, the bounce (variable two) decreases.

A (Cars that are older tend to have higher mileage) YOUR ANSWER

This statement illustrates a positive correlation, not a negative one. As the age of the car (variable one) increases, the mileage (variable two) also increases. Therefore, this is not a negative correlation where one variable increases as the other decreases.

B (Tennis balls that are older tend to have less bounce) CORRECT

This statement represents a negative correlation. As the age of the tennis ball (variable one) increases, the bounce (variable two) decreases. This is a clear example of a negative correlation where an increase in one variable results in a decrease in the other.

C (Shorter people tend to weigh less than taller people) YOUR ANSWER

This statement does not necessarily demonstrate a negative correlation. While it may appear that as height (variable one) decreases, weight (variable two) also decreases, there are many other factors that could influence someone's weight. Therefore, this cannot be definitively categorized as a negative correlation.

D (People who play baseball more tend to have more hits) YOUR ANSWER

This statement illustrates a positive correlation, not a negative one. As the frequency of playing baseball (variable one) increases, the number of hits (variable two) also increases. Therefore, this is not a negative correlation where one variable increases as the other decreases.

Conclusion

In summary, a negative correlation is where an increase in one variable results in a decrease in the other. The statement that older tennis balls have less bounce is the only choice that illustrates this relationship, with the age of the tennis ball increasing and its bounce decreasing. The other choices either show a positive correlation or cannot definitively be categorized as a negative correlation.

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