A study of the effects of television measured how many hours of television each of 125 grade school children watched per week during a school year and their reading scores. The study found that children who watch more television tend to have lower reading scores than children who watch fewer hours of television. The study report says that "Hours of television watched explained 9% of the observed variation in the reading scores of the 125 subjects." The correlation between hours of TV and reading score must be
A) r = 0.09.
B) r = -0.09.
C) r = 0.3.
D) r = -0.3.
E) Can't tell from the information given.

Question

Quizplus · Accepted Answer

The statement "Hours of television watched explained 9% of the observed variation in the reading scores" tells us the coefficient of determination (r-squared) between hours of TV and reading score is 0.09.

The coefficient of correlation (r) is the square root of r-squared. Therefore,

r = √0.09 = 0.3 (the negative sign indicates a negative correlation between hours of TV and reading score).

Therefore, the answer is D) r = -0.3.

A Study of the Effects of Television Measured How Many