A Medical Researcher Is Interested in How Weight Gain in Children

Multiple Choice

A medical researcher is interested in how weight gain in children from third-world countries is affected by the source of protein (fish, roots and tubers, or nuts and oilseeds) and by level of protein intake (low, defined as less than 0.56 grams per kilogram of weight, or high) .The researcher wants to test the relative efficacy of each protein source, controlling for the level of protein intake but not testing it as the main variable of interest.For this purpose, she classifies a group of children in an impoverished village in a third-world country into either high or low protein intake.Then, the researcher randomly assigns 50 children from each category to a group where the children will receive food once a day that will emphasize one of the three protein sources.You can assume that the total level of protein intake is not affected (its effects take a longer time to show and depend largely on the other meals the children have at home) .The researcher's alternative hypothesis is ______.

A) $\mu$ ₁ $\neq$$\mu$ ₂ $\neq$ $\mu$ ₃
B) $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
C) $\mu$ ₁= $\mu$ _{2= $\mu$ 3
D) at least one of the average weight gains will be different than the others
E) $\mu$ 1 $\mu$ 2 ≥ $\mu$ 3}