Question

The authors of a paper studied the relationship between y = arch height and scores on a number of different motor ability tests for 218 children. They reported the following correlation coefficients. Motor Ability Test Correlation between Test Score and Arch Height Height of Counter Movement Jump -0.03 Hopping: Average Height -0.09 Hopping: Average Power -0.06 Balance, Closed Eyes, One Leg 0.05 Toe Flexion 0.10 (a) Identify the value of the correlation coefficient between average hopping height and arch height. Interpret the value of the correlation coefficient. There is a weak negative linear relationship between average hopping height and arch height. There is a strong negative linear relationship between average hopping height and arch height. There is no linear relationship between average hopping height and arch height. There is a strong positive linear relationship between average hopping height and arch height. There is a weak positive linear relationship between average hopping height and arch height. What does the fact that the correlation coefficient is negative say about the relationship? Do higher arch heights tend to be paired with higher or lower average hopping heights? The negative correlation tells us that higher arch heights are associated with higher hopping heights heights. The negative correlation tells us that higher arch heights are associated with lower hopping heights heights. The negative correlation doesn't tell us whether higher arch heights are associated with higher or lower hopping heights heights. (b) The title of the paper suggests that having a small value for arch height (flat-footedness) is not a disadvantage when it comes to motor skills. Do the given correlation coefficients support this conclusion? Explain. No. Since all five correlation coefficients are close to 0.5, the results imply that there is a very strong relationship between arch height and the motor skills measured. No. Since all five correlation coefficients are close to 1, the results imply that there is a very strong relationship between arch height and the motor skills measured. No. Since all five correlation coefficients are close to 0, the results imply that there is a very strong relationship between arch height and the motor skills measured. Yes. Since all five correlation coefficients are close to o, the results imply that there is very little relationship between arch height and the motor skills measured. Yes. Since all five correlation coefficients are close to 1, the results imply that there is very little relationship between arch height and the motor skills measured.

Answer 1

a. The value of the correlation coefficient between average hoping height and arch height

r = -0.09

• There is a weak negative linear relationship between average hoping height and arch height.

• The negative correlation tells us that higher arch heights are associated with lower hopping heights.

b. Yes. Since all five correlation coefficients are close to 0, the results imply that there is very little relationship between arch height and the motor skills measured.