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. Which of the... 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. 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? Read more

Steps to Solve

1. Understand the correlation coefficient The correlation coefficient (denoted as $r$) measures the strength and direction of a linear relationship between two variables. It ranges from $-1$ to $1$.

2. Identify the type of relationship Since the problem states there is a "strong negative linear relationship" between the hours of exercise and resting heart rate, we can infer that as the hours of exercise increase, the resting heart rate decreases.

3. Determine reasonable values for $r$ For a strong negative correlation, values of $r$ are typically close to $-1$. Therefore, we can rule out any positive correlation values (like $0.71$) and values close to $0$ (like $0.00$ or $-0.14$), as they indicate weak or no correlation.

4. Evaluate options for $r$ The remaining options are $-0.87$ and $-1.00$.

5. Select the most reasonable value While $-1.00$ indicates a perfect negative correlation, $-0.87$ suggests a strong negative correlation without being perfect. Thus, $-0.87$ is more appropriate for a real-world scenario where factors might vary.