Final answer:
The statement that there is a strong negative association between gas price and miles driven based on a correlation coefficient of 0.15 is false, as 0.15 indicates a very weak positive (not negative) correlation.The correct answer is false.
Step-by-step explanation:
The statement made by Steve that there is a strong negative association between gas price and miles driven, based on a correlation coefficient of 0.15, is false. A correlation coefficient close to 0 indicates a very weak linear relationship between the two variables.
A correlation coefficient ranges from -1 to 1, with 1 being a perfect positive correlation, -1 being a perfect negative correlation, and 0 indicating no correlation. The sign of the correlation coefficient indicates the direction of the relationship. In this case, because the correlation coefficient is positive (0.15), it suggests a weak positive relationship, not negative, between gas price and miles driven. Thus, as gas prices increase, there might be a very slight tendency for miles driven to increase, but this relationship is so weak that it could easily be due to chance or other factors.
As for the significance of the correlation, without additional information such as a p-value or sample size, it's impossible to definitively say whether the observed correlation is statistically significant. However, based on the low value of 0.15 alone, it is unlikely to be significant. If we square the correlation coefficient to get the coefficient of determination (r²), we find that only about 2.25% (0.15² approximately equals 0.0225) of the variance in miles driven can be explained by changes in gas prices, which reinforces the point that the relationship is not strong.