A local newspaper randomly selects 20 patrons of the Springwood Restaurant on a given Saturday night and has each patron rate the quality of his or her meal as 5 (excellent), 4 (good), 3 (average), 2 (poor), or 1 (unsatisfactory). When the results are summarized, it is found that there are 16 ratings of 5, 3 ratings of 4, and 1 rating of 3. Let M_d denote the population median rating that would be given by all possible patrons of the restaurant on the Saturday night.
a. Test H₀: M_d = 4.5 versus H_a: M_d > 4.5 by setting α = .05.
b. Reason that your conclusion in part a implies that we have very strong evidence that the median rating that would be given by all possible patrons is 5.