College

Researchers believe that an increase in lean body mass is associated with an increase in maximal oxygen uptake. A scatterplot of measurements from 18 randomly selected college athletes showed a strong positive linear relationship between the two variables. A significance test for the null hypothesis that the slope of the regression line is zero versus the alternative that the slope is greater than zero yielded a p-value of 0.04. Which statement is an appropriate conclusion for the test? (A) The p-value of 0.04 does not indicate that 4% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass. (B) The p-value of 0.04 does not indicate that 16% of the variation in maximal oxygen uptake for college athletes can be explained by the amount of lean body mass. (C) The strong positive linear relationship displayed in the scatterplot, along with a p-value of less than 0.05, indicates that college athletes with higher lean body mass tend to have higher maximal oxygen uptake. (D) The strong positive linear relationship displayed in the scatterplot, along with a p-value of less than 0.05, does not prove that an increase in lean body mass causes an increase in maximal oxygen uptake for college athletes. (E) A p-value of less than 0.05 does not indicate that the relationship displayed in the scatterplot is likely due to chance, and there is statistical evidence of a relationship between lean body mass and maximal oxygen uptake for college athletes. The correct statement, given the information provided and if choosing an option based on the correct understanding of p-value and statistical evidence, would be (C). This statement accurately conveys that there is statistical evidence to suggest a positive relationship between lean body mass and maximal oxygen uptake, without implying causation or explaining the variation in terms of the percentage (which is a common misconstruction of the p-value).

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