Question

Some people believe that musical activity (e.g. playing an instrument) enhances mathematical ability. 100 high school students were selected at random. For each student, musical activity was recorded in hours per week and mathematical ability was assessed by a test. The correlation coefficient was found to be 0.85. What is the relationship between musical activity and mathematical ability?

Answer 1

The correlation coefficient of 0.85 indicates a strong positive relationship between musical activity and mathematical ability. For a student who practices a musical instrument for five hours a week, the predicted math test score is 86.5.

Step-by-step explanation:

The correlation coefficient of 0.85 indicates a strong positive relationship between musical activity and mathematical ability. This means that as the number of hours per week spent playing a musical instrument increases, the scores on the math test also tend to increase.

For a student who practices a musical instrument for five hours a week, we can use the equation of the line of best fit to predict their math test score. Substituting 5 into the equation ŷ = 72.5 + 2.8x:

ŷ = 72.5 + 2.8(5) = 72.5 + 14 = 86.5

Therefore, it is predicted that the score on the math test for a student who practices a musical instrument for five hours a week would be 86.5.