Suppose a dining court has been redesigned and a survey is planned to assess if the new design is an improvement. It contains 8 questions and 7 point scales with scores less than 4 favoring the previous design and scores greater than 4 favoring the new design. You consider randomly surveying 100 patrons. The hypotheses are: 0: = 4 > 4 Suppose that you want the adequate power to detect a mean of at least 4.40. Assume = 1.5. a. Given = 0.025, for what values of sample mean will you reject 0? b. Using = 4.40, what is the probability that the sample mean will fall in the region defined in part (a)? c. Will a sample size of 100 give you adequate power? Explain your answer. d. Determine the sample size that gives your power near 0.80