Question

set of weights (pounds) and highway fuel consumption amounts (mpg) of nine types of automobile the linear correlation coefficient is found and the P-value is 0.011 statement that interprets the Pvalue and includes a conclusion about linear correlation The Pvalue indicates that the probability of a linear correlation coefficient that is at least as extreme is which is there is a linear correlation between weight and highway fuel consumption in automobiles so theresufficient evidence to conclude that

Answer 1

The P-value of 0.011 suggests that there is a significant linear correlation between weight and highway fuel consumption in automobiles

The P-value of 0.011 indicates that there is a 1.1% probability of observing a linear correlation coefficient that is at least as extreme as the one found between weight and highway fuel consumption in automobiles by chance alone. In other words, the P-value represents the likelihood of obtaining the observed correlation coefficient due to random variation, assuming that there is no true linear correlation between weight and fuel consumption.

Since the P-value is less than the typical significance level of 0.05 (or 5%), it is considered statistically significant. This means that there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.

To put it simply, the P-value suggests that the relationship between weight and fuel consumption is not due to chance, but rather indicates a genuine association between the two variables. This implies that as the weight of an automobile increases, the highway fuel consumption tends to change in a predictable manner.

In conclusion, based on the given information and the low P-value of 0.011, we can confidently state that there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.