3. The dataset GRADESINTROSTATS is a file that contains information from a random sample of 31 students who took Statistics at MacEwan University in a recent term. Your variables of interest are LCMT (lecture midterm grade) and LCFE (lecture final exam grade). The data are given below; your instructor has calculated a column of differences for you. LCMT LCFE LCMT-LCFE 81.58 69.74 11.84 68.42 68.42 0 71.05 65.79 5.26 60.53 60.53 0 65.79 68.42 -2.63 55.26 61.84 -6.58 63.16 69.74 -6.58 84.21 50.00 34.21 89.47 88.16 1.31 81.58 73.68 7.9 92.11 78.95 13.16 86.84 84.21 2.63 97.37 81.58 15.79 68.42 63.16 5.26 68.42 68.42 0 52.63 65.79 -13.16 63.16 60.53 2.63 97.37 98.68 -1.31 68.42 60.53 7.89 78.95 84.21 -5.26 73.68 64.47 9.21 86.84 80.26 6.58 52.63 56.58 -3.95 50.00 71.05 -21.05 78.95 76.32 2.63 44.74 68.42 -23.68 73.68 76.32 -2.64 71.05 65.79 5.26 71.05 57.89 13.16 81.58 67.11 14.47 68.42 59.21 9.21 Note: the sample mean xa =2.630968 and the sample standard deviation sa = 11.05528. The student may verify this with R or Excel or an online calculator, if desired, but it is not necessary.