Question: A cereal company claims that their new cereal boxes include at least 50g more cereal than their old boxes. A consumer advocacy group tests this claim by weighing the contents of 70 randomly chosen old and new boxes of cereal. The mean weight for the new cereal boxes is 386g with a standard deviation of 12g, and the mean weight for the old boxes is 340g, with a standard deviation of 9g.

(a) State the null and alternative hypotheses.

(b)Perform the hypothesis test, using a p-value approach. What statement can the consumer advocacy group make about the cereal company’s claim?

c) Describe in words what is the Type I error for this test. What is the probability of Type I error given the type of test performed? Describe in words what the Type II error would be.