Question

All but one of the following statements contains a blunder. Which statement is correct?

A. We found a correlation of r = -0.63 between gender and political party preference.
B. There is a correlation of 0.54 between the position a football player plays and their weight.
C. The correlation between the gas mileage of a car and its weight is r = 0.71 miles per gallon.
D. The correlation between planting rate and yield was found to be r = 1.23.
E. We found a high correlation (r = 0.91) between the age and height of children

Answer 1

The correct statement about correlation is E. We found a high correlation (r = 0.91) between the age and height of children. This is the only statement that presents a correlation coefficient within the possible range and appropriately matches types of variables that can be expected to have a linear relationship.

Step-by-step explanation:

The question revolves around identifying which statement correctly represents a plausible correlation coefficient and understanding the interpretation of correlation values. A correlation coefficient (r) quantifies the strength and the direction of the linear relationship between two variables and is always within the range from -1 to +1. Values close to +1 or -1 indicate a strong linear relationship, while a value of 0 indicates no linear relationship.

Here are the reasons behind the incorrect options:
A.correlation cannot be computed between gender (nominal variable) and political party preference (another nominal variable).
B. The position a football player plays is a nominal variable and cannot be correlated with a continuous variable such as weight.
C. r should not have units (miles per gallon), as it is a dimensionless value.
D. r cannot be greater than +1, so a value of 1.23 is impossible.

The correct statement is: E. We found a high correlation (r = 0.91) between the age and height of children. This is a plausible correlation as it falls within the acceptable range of -1 to +1, and it makes sense that there could be a strong positive correlation between the age and height of children, as generally, children grow taller as they age.