Mice For a biology project you measure the tail length centi

Mice. For a biology project, you measure the tail length (centimeters) and weight (grams) of 12 mice of the same variety.

1. Explain why you expect the correlation between tail length and weight to be positive.

2. The mean tail length turns out to be 9.8 centimeters. What is the mean length in inches? (There are 2.54 centimeters in an inch.)

3. The correlation between tail length and weight turns out to be r = 0.6. If you measured length in inches instead of centimeters, what would be the new value of r?

Solution

1. Correlation between X and Y is positive implies that as X increases, Y increases and vice-versa. So, mice with longer tails imply a bigger size of their body and hence, more weight. Hence, weight and tail length are positively related and hence, correlation is positive.

2. Mean in inches = 9.8 / 2.54 = 3.8583 inches

3. Correlation does not change with change in units as correlation is a unitless measurement.

So new value of r = 0.6