Question 11

There is a positive correlation between stopping distance and speed.

The analysis of the scatterplot indicates that as the speed of the cars increases, the stopping distance also increases, demonstrating a positive correlation between the two variables.

A) There is no correlation between stopping distance and speed.

This option is incorrect because the scatterplot clearly shows a trend where stopping distance changes with varying speeds, indicating that there is indeed a relationship between the two variables.

B) There is a negative correlation between stopping distance and speed.

This option is also incorrect as a negative correlation would suggest that as speed increases, stopping distance decreases. However, the scatterplot demonstrates the opposite trend, confirming that higher speeds result in longer stopping distances.

C) There is a positive correlation between stopping distance and speed.

This option is correct because the scatterplot illustrates that as speed increases, the stopping distance correspondingly increases, which characterizes a positive correlation between these two variables.

D) The stopping distance of a car may be predicted perfectly from its speed.

This option is not correct as it implies a perfect linear relationship, which is rarely the case in real-world data. The scatterplot may show a positive correlation, but it does not indicate that stopping distance can be predicted perfectly from speed due to inherent variability in the data.

Conclusion

The correct answer, which highlights the positive correlation between speed and stopping distance, is supported by the observable trend in the scatterplot. All other options fail to accurately represent the relationship depicted, either by denying the correlation or misrepresenting its direction or predictability. Thus, option C is the definitive choice that aligns with the data's implications.