College dining facilities. University and college food service operations have been trying to keep up with the growing expectations of consumers with regard to the overall campus dining experience. Because customer satisfaction has been shown to be associated with repeat patronage and new customers gained through word of mouth, a public university in the Midwest took a sample of patrons from its eating establishments and asked them about their overall dining satisfaction.11 The following table summarizes the results for three groups of patrons: Category x n s Studentmeal plan 3.44 489 0.804 Facultymeal plan 4.04 69 0.824 Studentno meal plan 3.47 212 0.657 a. Suppose food service operations had been interested in comparing faculty on the meal plan to students overall. Use the results in the table to test this contrast. Make sure to specify the null and alternative hypotheses, test statistic, and P-value