Problem 1. {15 points, 4 parts) A box of cereal, by spec, is supposed to have 368 grams of cereal, on average. To check whether the cereal lling process is to spec, 25 boxes of cereal are sampled. Assume that the population standard deviation is known to be 15 grains. Also, assume that the amount of cereal in a box is Normally distributed. In answering the following questions. consider a 5% level of signicance and the null hypothesis Hm : p. E 368. In practice, we cannot know the population mean, but we may perform a whatif analysis. For the following three whatif scenarios, determine both {i} the probability of a Type I error and (ii) the probability of a Type II error: e} ,u. = 364 45) gr = 368 (3) gr = 3611) Finally, d} Use Excel to plot the power curve. (Hint: A scatter plot may make sense.) Please copy and paste your plot into W'ord