4. Imagine that you are writing a proposal to get some funding from a local school district board to study whether the game of "scatterball" has better child mental health outcomes than the traditional game of "dodgeball" during PE class (both games involve the children throwing a ball at each other, but in scatterball, no one is tagged "out" of the game). Specifically, you plan to randomly assign third-grade children from a local school to one of three groups: one group will play scatterball during PE every day for a week, one group will play traditional dodgeball during PE every day for a week, and one will play a completely different sport outside during PE every day for one week (volleyball). At the end of one week, you plan to measure each child from the first two groups on their mental health wellness using a mental health scale that has a population variance 2 = 400 (the third group is not going to be measured and won't be part of your comparison so that you can keep $$ costs down as much as possible). You believe, based on prior research, that mental health for the first group (that played scatterball) will be +30 points better than the second group (that played traditional dodgeball). Your initial plan is to have n=8 students in group 1 and n=8 students in group 2. Assuming your belief that there is a true difference between groups 1 - 2 = +30 points, evaluate your power with n=8 students/group. This will be a picture of two sampling distributions that overlap. Us