Question

A sample of automobiles traveling on a particular segment of a highway is selected. Each one travels at roughly a constant rate of speed, although speed does vary from auto to auto. Let \(x=\) speed and \(y=\) time needed to travel this segment. Would the sample correlation coefficient be closest to \(0.9,0.3,-0.3,\) or \(-0.9 ?\) Explain.

Short answer

The sample correlation coefficient would most likely be closest to \(-0.9\), indicating a strong inverse relationship between speed and time.

Step-by-step solution

Understand the relationship between variables

Determine the relationship between the variables. The relationship between speed (x) and time (y) is inverse or negative. As one increases, the other decreases.

Correlation analysis

On analyzing the correlation options given, we can rule out the positive values \(0.9\) and \(0.3\) as they represent a positive correlation. We are left with two options, \(-0.9\) and \(-0.3\). A correlation of \(-0.9\) indicates a strong negative correlation while \(-0.3\) indicates a weak negative correlation.

Determine the most likely correlation

Since we know the relationship between speed and time is a strong inverse one, based on real-life experience, we can assume that the correlation coefficient would be closer to \(-0.9\) rather than \(-0.3\).