5. (25 pts) In a large study, 942 women were surveyed and their daily dietary intake of Calcium, Iron, Protein, Vitamin A, and Vitamin C were recorded. Since we have 5 quality charac- teristic, p = 5. The sample average and sample covariance matrix for the dietary intake are: 624.0 mg 11.1 mg 157829.4 940.1 6075.8 102411.1 6701.6 940.1 = 65.8 g and S= 35.8 114.1 6075.8 114.1 934.9 2383.2 137.7 7330.1 477.2 839.6 g 78.9 mg 6701.6 137.7 477.2 102411.1 2383.2 7330.1 2668452.4 22063.3 22063.3 5416.3 The recommended intake of these nutrients are: 1000 mg 15 mg Lo = 60 g 800 75 mg Conduct hypothesis test (with a = 0.01) to verify if the average dietary intake meets the recommendations. Although it is not needed, you may check the data related to this problem on canvas Assignment 6 folder (Women's survey data).