The auto insurance industry crashed some test vehicles into a cement barrier at speeds of 5 to 25
Mph to investigate the amount of damage to the cars. They found a correlation of r = 0.60 between
Speed (MPH) and damage ($). If the speed at which a car hit the barrier is 1.5 standard deviations
Above the mean speed, we expect the damage to be _?__ the mean damage.
A) 0.90 SD above
B) 1.5 SD above
C) equal to
D) 0.36 SD above
E) 0.60 SD above

Question

Quizplus · Accepted Answer

The correlation coefficient is 0.60, which means that there is a moderate positive correlation between speed and damage. This means that as speed increases, damage also tends to increase. The mean speed is not given, but we are told that the speed at which a car hit the barrier is 1.5 standard deviations above the mean speed. This means that the speed is 1.5 * SD above the mean. We can use the correlation coefficient to predict the amount of damage that we would expect to see at this speed. The expected damage is equal to the mean damage plus 0.60 * 1.5 * SD = 0.90 SD above the mean.

The Auto Insurance Industry Crashed Some Test Vehicles into a Cement