Homework Question 1 Imagine that you are writing a grant proposal in which you plan to randomly assign low-performing third- grade children to receive one of two types of after-school tutoring interventions: either a meaningfocused intervention (practicing what the meaning; of word parts of are) or a decodingfocused intervention (practicing how to round out word parts). Each group will receive their assigned intervention for three months. At the end of the intervention, you plan to measure each group's reading comprehension ability with a particular test that has a population mean of 400 and a population variance of 800. You believe, based on prior literature, that comprehension scores of the meaning-focused intervention will be 20 points higher than scores of the decoding-focused intervention. Your initial plan is to use n=16 students in each of your intervention groups. a) Assmning your belief that the alternative is that there is a true difference between groups of 20 points, sketch a picture of what these two distributions look like (the null and the alternative) using (1:05 (2 tailed). Use the steps discussed in class: (i) draw the null distribution, (ii) label the upper limit and lower limit for your critical regions, (iii) draw the alternative distribution, and (iv) nd the area in the alternative distribution you consider as power and shade it in. b) Examine your sketch in part #a. i. What is your approximate power (this is the shaded area)