CPM Homework Help : CC3MN Problem 8-50

Scientists consider the average growth rate of kelp (which grows in the sea) and the average mass of crabs that live in kelp beds to be indicators of the health of marine life. But they want to know if there is an association between the growth rates of kelp and the masses of crabs.

Marine biologists collected data from different parts of the world and created the following conditional relative frequency table. They considered the average growth rate of kelp as the independent variable.

$\%$ CRABS

Average Mass of Crabs (kg)

$\mathbf{< 0.25}$

$\mathbf{0.25} \; \text{-} \; \mathbf{0.49}$

$\mathbf{0.50} \; \text{-} \; \mathbf{0.75}$

$\mathbf{> 0.75}$

Average
Growth Rate
of Kelp
(cm/day)

$\mathbf{< 5}$

Average Growth Rate of Kelp is < 5 and average mass of Crabs is < 0.25: $66\%$

Average Growth Rate of Kelp is < 5 and average mass of Crabs is 0.25 to 0.49: $34\%$

Average Growth Rate of Kelp is < 5 and average mass of Crabs is 0.50 to 0.75: $0\%$

Average Growth Rate of Kelp is < 5 and average mass of Crabs is > 0.75: $0\%$

$\mathbf{≥ 5}$

Average Growth Rate of Kelp is greater than or equal to 5 and average mass of Crabs is < 0.25: $12\%$

Average Growth Rate of Kelp is greater than or equal to 5 and average mass of Crabs is 0.25 to 0.49: $49\%$

Average Growth Rate of Kelp is greater than or equal to 5 and average mass of Crabs is 0.50 to 0.75: $35\%$

Average Growth Rate of Kelp is greater than or equal to 5 and average mass of Crabs is > 0.75: $4\%$

Is there an association between growth rates of kelp and the masses of crabs?

Hint:

When the growth rate of the kelp is high, how are the crab masses distributed?
What about when the growth rate of the kelp is low?
What does this tell you about the association?