Question

for a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. for the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?
a 0.71
b 0.00
c -0.14
d -0.87
e -1.00

Explanation:

Step1: Understand correlation concept

Correlation coefficient \(r\) ranges from - 1 to 1. Positive \(r\) means positive linear relationship, negative \(r\) means negative linear relationship.

Step2: Identify relationship type

Since those who exercise more hours per week tend to have lower resting heart - rates, it is a negative linear relationship, so \(r<0\).

Step3: Determine strength of relationship

It is a strong linear relationship. The closer \(|r|\) is to 1, the stronger the linear relationship. Values close to 0 indicate weak linear relationships.

Answer:

D. -0.87