Question

4.2 ap-8
describe a real situation that will show a negative linear association.
choose the correct answer below.
a. the speed and the driving time of a trip
b. the distance and the driving time of a trip
c. the age of a child and the childs height
d. the size of a pool and the amount of water it takes to fill it

Explanation:

To determine a negative linear association, we analyze each option:

• Option A: As speed increases, driving time (for a fixed distance) decreases. This shows a negative linear relationship (since \( \text{time} = \frac{\text{distance}}{\text{speed}} \), so time and speed are inversely related linearly for constant distance).
• Option B: Distance and driving time (at constant speed) have a positive linear association (\( \text{distance} = \text{speed} \times \text{time} \), so as time increases, distance increases).
• Option C: A child's height generally increases with age, showing a positive association.
• Option D: Larger pool size requires more water to fill, showing a positive association.

So only Option A has a negative linear association.

Answer:

A. The speed and the driving time of a trip