Question

Which of the following statements is not true of the correlation r between the lengths (in inches) and weights (in pounds) of a sample of brook trout?

a. r must take a value between −1 and 1.

b. r is measured in inches.

c. If longer trout tend to also be heavier, then r > 0.

d. r would not change if we measured the lengths of the trout in centimeters instead of inches.

e. r would not change if we measured the weights of the trout in kilograms instead of pounds.

Short answer

The correct option is (b) $r$ measured in inches.

Step-by-step solution

Given information

The lengths (in inches) and weights (in pounds) of a sample of brook trout were correlated $\left(r\right)$.

Explanation

One of the statistical measurements of the strength of the relationship between two variables is the correlation coefficient. It does not have a specific unit. It establishes the boundaries between two numerical values of $-1$ and $1$ It cannot be measured in any unit, including inches, and it has no effect when shifting from one unit to another, such as inches to centimeters and pounds to kilograms.

Hence, the correct option is (b)