2. The mean daily energy requirement for eight-year-old boys is 2200 calories. An education researcher believes many students in this group do poorly in school due to an inadequate diet and not having enough energy. A random sample of 37 academically at-risk eight- year-old boys was obtained, and their caloric intake was carefully measured for one day. The mean caloric intake of these 37 boys is 2089. Assume the standard deviation of caloric intake of all eight- year-old boys is 358 and the caloric intake of all eight-year-old boys follows the normal distribution. Is there any evidence this group of students has a mean caloric intake below the daily energy requirement? Use q=0.05. (a) Formulate the null and alternative hypotheses. (b) Compute the appropriate test statistic. (c) Produce a sketch of the rejection region(s) with the critical value(s) labelled. (d) Compute the P-value. (e) State your conclusion (reject or fail to reject the null hypothesis). (f) Interpret your conclusion in context