A researcher studies the effects of 3 different diets on weight gains in rats. She chooses 12 rats at random (from a large population) and assigns...

A researcher studies the effects of 3 different diets on weight gains in rats. She chooses 12 rats at random (from a large population) and assigns the rats to exactly one of the 3 diets. She also records the covariate x (initial weight), because she knows the response y(weight gain) will depend on x. Assume that 4 rats are assigned to each diet.

a) Suppose we wish to test for whether the slope is significant using  alpha= 0.05. Describe clearly how to do this. State the alternatives and the decision rule.