simple R studio homework

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pknpzl

Mathematics

University of California - Davis

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all the data will be attached. want to results in HTML file.

attach the question.(just the R studio part)

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height hsGPA 72 75 73 65 70 69 68 70 73 64 67 72.5 63 67 59 64 68 69 68 72 62 68 64 69 66 71 64.5 66 68 65 75 74 74 70 80 77 68 70 68 78 66 71 71 pulse 3.1 3.96 2.7 3.78 3.502 3.88 3.2 3.6 3.76 3.9 4 3.2 4 4 3.5 4 3.93 3.8 3.86 4 3.86 3.93 3.5 4 3.5 2.8 3.4 3.93 3.79 4 3.2 3.2 3.7 3.46 3.2 3 3.8 4 3.98 3.8 3.01 3.85 3.2 90 56 56 80 72 66 75 60 68 76 72 120 92 86 66 65 65 78 64 90 150 60 68 68 78 60 98 66 90 80 52 72 60 55 60 79 74 62 60 72 50 110 55 68 62 77 73 66 72 68 66 70 67 66.5 71 70 66 68 70 75 69 70.75 70 72 70 63 71 65 69 74 70 68 64 65 66 69 60 64 65 63 71 63 64 64 68 63 69 3.995 3.98 3.5 3.14 3.8 3 3 3.6 3.5 4 3.98 3.5 3.4 3.5 3.6 3.75 3 3.4 3.98 3.97 3.8 3.5 3.992 3.86 3.3 3.86 3.9 3.8 4 3.9 3.8 3.6 3.7 3.99 3.92 3.98 3.8 3.6 3.85 3.9 3.8 3.6 3.9 4 78 60 80 72 40 92 64 64 64 88 100 88 52 72 80 80 68 64 68 72 72 60 56 80 78 60 60 60 80 60 60 60 60 90 90 70 90 66 60 100 80 60 60 60 68 68 68 74 69 64 67 65 73 68 67 67 73 73 64 60 71 71 66 66 66 67 72 76 62 68 74 62 68 67 74 65 72 67 70 67 71 73 65 67 64 75 70 69 3.98 4.42 3 3.27 3.1 3.6 3.5 3.78 3.35 3.75 3.2 3.65 3.45 3.5 3.3 3.7 3.5 3.4 3.993 3.8 3.4 3.9 3.78 2.76 3.6 4 3.8 4.2 3.3 3 3 3.471 2.75 3.4 3.3 3.6 3.9 3.75 3.7 3.1 3.8 3.45 3.8 3.7 80 90 70 75 72 60 90 100 80 90 90 60 60 70 120 80 70 80 80 110 56 60 60 70 78 60 68 68 66 90 70 69 70 60 72 68 74 50 75 64 56 72 52 76 67 62 64 67 67.5 63 67 72 65 63 63 71 74 69 69 68 70 66 65 61 72 68 68 69 72 65 66 69 75 74 72 69 71 72 70 70 68.5 69 63 67 66 71 64 67 3.92 3.7 3.7 3 3.3 3.9 4 3.85 3.7 3.78 3.8 3.2 3.92 3.9 2.58 2.97 3.85 4 3.7 4.7 4 4 3.6 3.2 3.5 3.89 3.96 3.3 3.956 3.1 4 4 3.96 3.4 3.76 3.6 3.65 3.82 3.984 3.85 3.3 4 3.98 3.88 68 84 80 88 56 60 88 68 69 76 52 84 56 64 72 96 72 64 68 70 80 80 70 80 72 120 60 80 90 88 72 66 72 70 86 60 110 60 84 60 42 114 90 70 64 73 66 67 68.75 72 70 65 65 65 65 65 63 67 64 64 60 78 69 60 72 68 65 67.5 68 73 75 71 66 69 66 66 62 61 64 68 68 68 66 70 65 72 65 70 3.4 3.67 3.9 3.98 3.98 3.1 4 3.8 3.8 3.95 3.93 3.7 3.7 3.769 3.9 3.8 3.74 3.4 3.85 3.91 3.95 3.89 3.75 3.66 3.86 2.8 3.5 3.5 3.58 3.85 3.9 3.82 3.99 3.985 3.76 3.8 3.8 3 3.56 3.75 3.92 3.69 3 3.98 72 58 72 78 90 102 96 88 78 80 84 96 110 140 88 75 90 85 64 90 60 65 60 80 60 50 98 70 80 80 60 80 60 104 82 160 54 70 60 78 65 72 70 70 71 72 71 75.5 64 73 78 67 66 67 72 69 72 63 64 67 64 70 72 65 71 71 72 66 67 70 69 72 64 62 67 72 67.5 66 56 74 67 67 65 71 72 63 69 64.5 3.94 3.8 3.9 3.94 3.84 3.8 3.5 3.8 3.6 4 4 3.8 3.8 3.97 3.98 3.4 3.85 3.9 3.98 3.58 3.9 3.5 3.6 3.2 4 3.5 3.5 2.8 3.87 4 3.3 3.67 3.94 3.75 3.985 3.9 3 3.3 3.75 3.6 3.95 3.9 3.5 3.85 70 61 90 64 80 75 60 78 72 64 70 60 60 70 100 90 120 84 85 110 80 80 75 85 80 75 70 72 80 80 180 72 70 75 76 90 69 80 69 70 48 74 66 80 64 73 77 67 64 68 71 82 66 65 70 71 70 63 64 71 66 66 70 67 63 66 67 64 66 70 67 66 71 72 63 71 67 68 69 69 64 63 68 72 62 64 65 71 3.9 3.9 3.65 3.8 3.9 3.7 3.2 3.4 3.5 3.93 3.5 3.4 3.8 4 4 4 4 3.8 3.9 3.9 3.5 3.7 3.98 4 3 4 3.822 4 3.65 3.4 3.8 3.97 4.03 3.88 4 3 3.75 3.2 3.8 3.1 3.6 3.9 3.63 2.7 60 60 50 54 60 60 20 90 96 86 70 80 60 80 80 80 60 70 90 50 90 70 60 110 60 64 80 80 61 78 70 60 54 70 140 60 110 120 90 88 68 48 80 80 68 70 65.5 64 71 73 67 70 76 77 70 62 71 67 75 68 62 69 69 69 65 68 67 63 66 63 73 65 73 69 65 63 73 65 68 75 74 69 69 66 66 65 72 73 3.4 3.3 3 3.67 3.33 3.67 3.2 4 3 3 3 3.99 4.1 3.4 4 3.9 3.2 3.98 3.6 3.69 3 3.89 3.9 3.4 4 3.4 3.987 3.9 3.1 3.96 3.36 3.4 3.6 3.2 3.4 3.5 3.6 3.5 3.3 4 3.9 3.8 3.95 3.2 76 60 84 48 92 76 60 66 56 72 60 60 88 68 56 110 80 110 60 80 100 65 60 90 95 90 60 60 90 70 70 70 64 72 72 66 66 72 84 66 54 90 78 90 75 74 70 78 67 65 62 66 72 69 66 67 70 63.5 73 63 62 70 67 72 60 71.25 73 67 70 61 62 68 62 68 75 63 67 70 64 67 64 69 71 60 62 74 73 74 3.4 4.6 3 3.9 3.925 3.9 3.75 3.2 3.7 3.4 3.8 3.72 3.75 3 3.3 4 3.6 3.72 3 4 3.5 3.86 2.65 4 3.7 3.98 3.9 3.8 3.92 3.78 3.4 3.6 3.3 3.8 3.83 3.85 3.8 3.7 3.91 3.96 3.4 3.4 3.8 3.48 72 72 78 96 60 90 84 72 72 90 66 90 72 90 78 90 72 114 72 78 72 90 78 90 72 60 80 100 76 72 60 102 116 68 67 118 96 84 80 60 84 78 80 84 69 70 67 68 71 67 74 64 66 63 62 68 74 63 78 69 69 75 64 58.5 68 67 68 71 76 66 67 66 70 63 69 69 64 66 73 63 71 71 63 64 70 63 74 73 3.9 2.1 3.25 3.5 3.759 3.75 3.6 3.96 3.7 3.7 3.7 3.6 3.8 4 3.7 3.6 3.5 3.95 3.6 3.83 3 3.7 3.85 3.33 3.7 3.99 3.4 4 3.1 3.98 3.92 3.86 4.2 4 3.4 3.76 2.6 3.5 3.5 3.6 3.3 3.5 3.7 3.45 74 66 80 60 60 80 64 84 96 44 80 75 70 78 68 72 72 84 88 78 50 65 60 40 60 90 66 130 40 68 75 91 72 64 68 90 74 54 70 60 78 71 92 84 65 70 71 72 72 62 66 66 64 66 68 69 68 63 77 65.5 64 74 64.5 60 76 69 59 66 66 69 72 72 72 70 74 76 66 65 70 64 62 60 66 66 73.5 59 62 60 3.8 3.98 3.985 3.8 3.7 3.9 3.9 3.9 4 4 3 3.8 3.5 3.7 3.18 3.9 3 3.8 3.75 3.3 4.42 3.5 3.4 3 3.82 3.3 3.5 3.39 3.75 3.6 3 3.78 2.6 4 3.76 3.4 3.89 3.8 3.9 3.6 3.7 3.4 3.94 3.958 60 70 70 90 80 150 110 100 80 50 50 60 50 150 90 90 80 60 90 100 70 70 68 60 110 80 54 90 50 50 60 80 80 80 100 90 80 71 80 80 80 90 80 80 63 72 70.5 74 67 72 70 72 71 66 71 73 68 75 72 71 68.5 74 68 73 64 70 73 72 70 70 64 72 62 68 64 64 68.5 67 74 76 73 65 73 66 60 63 67 70 3.5 3.84 3.5 3.53 3.4 3.57 2.8 3.67 3.98 3.8 3.02 3.7 3 3.79 3.5 2.6 3.8 3.9 3.85 2.85 3.7 3.9 3.94 3.33 3.9 3.74 3.4 3 3.54 3.7 4 3.7 3.8 3.5 3.6 3.87 3.68 2.8 3.5 3.46 3.38 3.77 3.85 3 68 60 68 60 84 56 100 64 76 76 80 84 92 68 64 70 62 60 56 68 77 60 60 80 60 64 95 50 54 60 60 50 72 64 7 75 100 62 65 63 79 84 80 70 74 73 68 68 65 68 73 67 68 66.5 71 73 67 65 66 76 66 64 74 62 64 70 70 68 72 63 64 71 70 77 71 66 65 61 63 66 72 69 73 74 69.75 73 74 64 3 3.6 4 3.44 3.7 3.6 3.8 3.38 3.4 3.9 4 2.9 3.75 3.98 3.3 3.9 3.8 3.6 3.2 3.8 3.89 3.3 3.04 3.5 3.2 3.9 3.9 3.39 3.97 3.8 3.8 3.8 3.8 3.9 3.5 4 3.5 3.2 3.71 2.7 3.8 3.6 4 3.69 59 78 80 66 120 90 150 110 60 114 33 66 50 76 90 60 80 90 60 80 70 55 75 85 78 80 70 62 60 110 80 90 80 100 60 100 60 70 80 60 60 60 72 65 63 70 68 75 69 66 62 65 74 69 67 73 66 74 67 69 76 75 70 65 65 68 62 67 71 74 64 62 67 68 72 68 73 70 69 69 69 66 69 63 65 62 75 73 3.9 3.42 3.6 3.7 2.5 3.6 3.6 3.4 2.85 3.89 3.7 3.2 3.8 3.89 4 4 3.7 3.5 3.8 3.7 3.85 3.8 3.75 3.9 3.945 3.15 3.8 3.3 3.7 3.9 2.4 3.93 3.59 3.5 3.79 3.7 3.3 3.7 3.86 3.57 3.85 4 3.3 3.7 68 65 70 90 100 80 70 100 90 60 100 100 90 120 90 95 60 90 110 54 60 55 62 50 70 65 100 60 101 60 80 50 70 80 60 60 90 67 70 60 80 70 70 75 74 68 65 67 62 67 67 72 66 70 68 75 69.5 68 72 74 68 75 71 72 73 64 74 70 71 64 64 68 59 65 66 70 72 75 67 74 67 71 62 70 72 62 71 64.5 3 3 3.65 3.6 3.9 2.8 3.9 3.2 3.3 3.4 3.79 2.8 3.55 3.4 3.87 3.2 3.5 3.4 3.2 3.8 2.3 3.9 3.65 3.83 3.94 3.85 3.25 3.4 3.5 3.7 3 3.5 3.3 3.2 3.5 3.4 3.4 3.31 3.6 3.7 4.2 3.9 3 3.78 80 52 100 70 80 60 120 130 90 70 72 56 48 85 64 76 72 84 84 68 45 95 60 68 64 72 68 88 80 80 76 70 60 50 70 66 12 70 78 70 72 72 60 120 70 66 72 66 73 63 64 66 70 68 74 68 63 68 63 70 71 65 67 76 71 65.5 64 64 69 65 72 70 66 56 67 68 67 72 63 63 69 64.5 72 71.5 66 61 61 64 3.5 3.8 3.9 3.89 3.3 3.9 3.9 3.65 3.4 4 3.3 3.82 4 3.65 4.032 3.4 3.2 4 3.8 3.73 3.4 3.89 3.8 3.4 3.5 3.89 3.3 3.97 3.87 4.2 3.7 4 4 3.5 3.6 3.5 3.98 3.7 3.5 3.9 3.6 3.4 3.9 3.95 90 80 64 56 80 84 71 72 84 70 65 53 78 65 54 60 75 67 70 74 70 62.5 52 115 52 70 62 70 70 50 120 85 75 70 60 92 69 80 84 72 68 80 80 80 76 60 69 71 69 63 68 70 64 61 64 65 66 69 69 65 67 75 68 72 70 70 72 73 66 68 67 63 70 72 74 69 62 75 70 70 74 72 72 69 72 60 68 75 3.1 3.3 3.4 3.3 3.43 4 3.8 3.85 3.84 3.9 3.78 3.6 3.5 4 3.5 3.6 3.87 3.8 3.4 3.54 3.5 3.94 3.25 3 3.57 3.6 3.4 3.7 3.48 3.72 3.78 3.67 3.991 3.2 3.89 4.21 3.3 3.8 4 3.65 3.41 3.09 3.6 3.97 60 96 88 60 80 80 52 88 100 88 60 76 84 88 72 88 80 80 72 75 88 64 96 80 96 132 64 73 80 76 80 80 72 64 84 84 80 58 110 55 90 77 33 65 67 68 70 76 70 68 63 66 70 69 68 66.5 68 69.5 64 66 72 71 64 68 70 73 66 62 66 70 63 60 62 64 65 72 66 65 66 68 69 75 64 74 60 67 67 62.5 3.8 3.86 2.7 3.9 3.3 3.8 3.75 3.4 3.9 3.64 3.98 3.5 3.7 3.8 3.8 3.8 3.8 3.6 4 3.4 3.97 4 3.94 3.97 4 4 3.7 3.93 3.92 3.97 4.082 4 4 4 3.8 3.89 3.7 3.875 3.75 3.7 3.9 3.6 3.8 3.8 76 84 90 80 50 100 90 60 80 80 80 100 60 110 120 60 70 60 111 60 100 100 90 80 160 80 100 90 90 120 90 60 90 90 100 100 70 80 100 90 90 100 100 120 69 68 72 64 71 67 68 69 64 71 66 72.5 76 68 67 68 70 63 64 72 67 71 72 72 73 66 63 72 70 61 68 70 68 60 63 65 58.5 68 66 60 64 68 68 74 4 3.8 3.88 3.54 3.7 3.5 3.79 3.15 3.98 3.8 3 3.67 3.8 4.2 3.5 3.34 3.7 3.4 3.5 3.5 3.4 4 2.9 3.7 2.8 3.9 3.15 3.2 3 3.67 3.8 3.7 3.3 3.9 3.9 3.7 3.6 3.2 3.5 3.6 3.3 3 3.6 3.5 90 100 80 90 50 70 90 70 90 100 80 60 60 65 80 80 80 80 70 70 80 100 54 72 72 170 42 72 54 100 90 78 66 42 72 100 72 90 78 66 84 63 80 60 72 67 64 68 72 71 67.5 64 70 64 66 71 68 72 74 71 74 65 72 72 63 67 68 70 68 67 66 70 67 73 67 70 69 71 70 70 66 62 70 67 61 68 75 68 3.39 3.2 3.8 3.4 3.7 2.8 4 3.8 3.885 3.93 3.8 3 4 3.2 3.3 3.5 3.8 3.7 2.8 3.3 3.942 3.9 3.25 3.5 3.4 4 4 3.8 3.725 3.9 3.7 3.98 3.75 3.25 3.5 3.8 3.98 3.6 3.6 3.98 3.65 3.96 3.4 3.92 75 60 110 44 60 50 55 80 90 50 85 68 62 56 70 67 59 55 80 62 60 58 160 80 64 57 0 120 80 55 0 80 79 80 90 68 65 54 110 55 68 60 50 62 67 65 73 77 65 73 68 75 73 67 67 66 65 68 68 56 70 70 72 71 67 70 72 72 68 67 68 67 68 65 64 64 73 60 73 72 70 65 65 65 73 62 66 70.5 3.89 3.97 3.2 3.75 3.85 3.5 3.7 3.87 2.7 3.7 3.8 3.9 3.7 3.63 3.8 3.4 3.5 3.6 3 3.2 3.65 3.75 2.75 4 3.1614 3.2 3.6 4.5 2.65 4 3.8 2.5 3.5 3.5 3 3.5 3.86 4 3.67 3.5 3.9 3.93 3.9 2.9 76 80 80 64 60 60 60 80 52 88 88 70 80 78 76 60 72 64 76 73 60 64 96 52 80 72 68 56 76 68 76 96 84 72 65 48 80 60 60 76 68 64 80 64 67 74 71 67 67 61 60.5 61 67 64 64 72 65 68 74 70 78 72 68 64 63 64 65.5 71 64 72 64 71 73 64 72 72 69 70 73 70 68 72 72 70 70 66 68 65 3 2.6 3.3 3.6 3.78 3.8 3.7 3.94 3.98 3.7 3.68 3.88 3.72 3.5 3.6 3.99 3.83 3.33 3.6 3.5 3.7 3.7 3.9 3.6 3.92 3.7 3.25 3.5 3.33 3.8 3.7 3.4 4 3 4 4 3.2 3.4 3.6 3.49 3.87 4 3.7 3.95 30 56 60 64 64 44 44 88 92 96 64 70 80 70 105 74 80 70 68 80 64 84 64 80 64 72 68 68 80 84 72 72 60 52 60 68 76 56 55 120 42 55 13 60 75 65 76 67 72 72 71 75 67 72.5 72 65 69 75 74 62 64 66 76 71 72 67 67 64 67 71 74 64 75 75 70 68 73 65 70 63 69 65 63 63 73 68 65 64 3.3 3.8 3.71 3.83 3.3 2.7 3.8 3.74 3.67 3.86 3.4 3.65 3.9 3.5 3.2 3.8 3.4 3.53 3.6 3.75 3 3.8 3.98 3.8 3.3 4 3.2 3.967 3.5 3.1 3.1 3.89 3.93 3.9 3.6 4 3.5 3.89 3.6 3.98 3 3.87 4 3.65 90 75 60 88 62 87 64 70 25 72 60 72 66 66 84 54 60 90 66 60 60 54 72 60 60 48 60 74 66 60 78 68 68 65 66 88 75 83 84 80 84 63 65 64 75 62 64 74 66 71 67 74 62 73 69 69 71 70 70 67 61 70 67 69 65 66 73 62 64 66 62 66 66 68 70 70 74 63 80 68 64 64 69 62 71 72 68 73 3 3.9 3.2 3 3.6 3.2 3 3.5 4 3.32 4 3.4 3.8 3.75 3.85 3.95 3.2 3.78 3.87 3.2 3.7 3 3.73 3.65 3.94 3.1 3.75 4.02 3.975 3.7 3.86 3 3.8 3.8 3.1 3.96 3.6 3.8 3 3.9 4 3.1 3.4 3.2 64 78 70 82 78 70 80 65 88 140 76 60 64 120 67 54 63 58 52 70 63 50 84 52 34 65 85 78 70 130 88 60 75 65 60 72 35 80 70 75 70 70 80 80 64.5 63 63 62 66 73 73 72 67 65 61 65 77 71.5 61.5 69 65 66 70 71 75 72 76.5 75 72 70 69 71 68 67 68 69 75 66 65 72 67 63 66 62 72 69 63 70 3.46 3.8 3.93 3.2 3.7 3.3 3.1 3.45 3.4 4 3.85 4 3.17 3 4 3.1 3.98 3.5 3.35 3.9 4.1 3.8 3.3 3.52 4 3.65 3.29 3.98 3.2 3.94 3.84 3.65 3.2 3.87 3.4 3.5 3.7 3 3.7 3.5 3.3 4 4 4 120 90 80 70 65 100 60 70 100 70 90 70 60 80 76 60 90 45 88 88 80 60 48 73 68 40 80 77 84 90 62 90 44 62 63 50 60 90 80 110 70 110 50 70 66.5 65 65 62.5 70 64 62 76 66 67.5 69 70 70 73 73 68 65 74 68.5 63 57 62 66 73 76 72 71 68 66 66 75 69 66 66 67 70 66 65 67 66.5 74 67 64 71 4 3.9 3.98 4 3.5 3.89 3.8 3.87 3.95 3.31 3.5 3.6 3.3 3.01 3.8 3.87 4 3.3 3.6 3.8 3.9 3.8 3.3 3 3.4 4 3.4 4 3.97 3.9 3.35 3.8 3.75 3.9 3.5 3.7 3.8 4.6 3.2 3.9 3.9 3.7 3.85 3.3 70 70 100 90 60 70 70 80 70 100 80 88 60 80 64 72 80 68 96 72 56 68 56 56 70 56 70 72 88 44 88 94 72 84 48 60 90 108 84 84 66 78 102 90 65 67.5 63 66 60 67 67 68 65 65 74 65 55 64 65 67 70 71 67.5 70 73 70 62 69 63 70 74 72 70 68.5 68 74.5 71 67 66 71 74 73 65 47 65 73 74 70 3.81 3.2 3.83 3.88 3.43 3.9 3.75 3.54 3 3.6 3.3 3.5 3.8 3.55 3.5 3.76 3.2 3.3 3.6 3.82 3.7 3.4 3.78 3.3 4 3.1 3.8 3.4 3.7 3.95 3.5 3.2 3.4 3.9 3.85 3.74 3.3 3.3 3.86 3.85 3.8 3.6 3.6 3.97 96 96 72 84 96 102 78 96 108 100 72 29 85 83 80 62 27 75 90 60 60 40 45 48 76 60 72 68 56 84 60 72 68 96 64 76 76 92 60 120 104 80 56 130 68 72 59.5 83 69 74 62 66 66 68 67 73 65 62.5 64 65 68 72 71 77 61 64 65 61 63 65 64 64 59 65 69 69 65 64 71 67 74 77 70 73 74 70 67 62 3.84 3.67 4.069 3.8 3.3 3.4 3.8 3.9 3.6 3.8 3.8 3.2 4 3.8 3.84 3.96 3.3 2.98 3.3 3.7 3.3 4.03 3.2 3.9 3.9 3.8 3.99 4.1 3.89 4 3.9 3.98 3.76 4 3.97 3.3 3.9 3.4 3.9 3.5 3.8 3.95 3.79 3.97 80 68 10 76 68 72 60 56 64 80 88 68 94 96 80 52 80 84 56 76 84 80 56 92 80 44 70 80 50 70 70 100 70 100 54 80 60 70 65 76 90 60 80 70 70 72 71 64 66 69 71 62 70 72 72 69 70.75 68 67 70 64 70 62 68 66 72 69 73 63 63 69 67 60 70.5 64 70 66 73 63 73 66 60 63 68 66 64 63 63 3.95 4 3.9 3.7 3.75 3.76 3 3.4 3.72 3.6 2.99 3 3 3.5 3.95 3.3 3.83 3.2 3.6 3.6 3.78 3.4 3.46 3.3 4.04 3.6 3.94 3.62 3.9 3.67 3.5 3.8 4 3 3.8 3.53 4 4.2 3.8 3.5 3.2 3.87 4 4 60 70 50 60 90 90 70 80 70 55 70 80 60 80 90 70 80 85 100 70 70 84 108 66 63 63 72 66 72 96 60 72 72 96 72 66 66 56 90 60 48 48 60 60 71 67 69 73 72 70 72 74.4 66 62 62 65 68 72 67 65 63 65 63.75 67 66 65 67 72 70 74 71 65 69 65 76 70 63 66 70 64 63 66 62 61 68 60 68 66 3.87 3.1 3.5 3.87 3.8 3.9 3.7 3.22 3.8 4 4 3.83 3.7 3.47 3.2 3.2 3.8 3.7 3.75 3.6 3.61 3.5 2.9 3.2 2.4 3.6 3.5 3.3 3.9 4.2 3.7 3.2 3.3 3.2 3.5 3.4 3.6 3.99 3.6 3.8 3.49 3.7 3.1 3.67 72 90 60 66 90 66 84 72 66 102 126 102 72 72 82 72 96 102 60 60 72 76 68 80 72 72 100 90 70 90 67 78 46 72 72 84 60 72 78 72 84 72 84 72 67 70.5 66 69 73 64 66 74.5 67 66 69 70 73 66 75 72 72 65 72 65 74 66 67 65 65 66 69 71.5 73 67 65 63 73.5 70 77 71 77 74 74 62 71 67 66 63 3.7 3.2 3.5 3.98 3.5 3.6 4 3.4 3.9 3.8 4.3 3.7 3.65 3.3 3.51 3.56 3.3 4 3.25 4.2 3 4 3.5 3.7 4 3.5 3.9 3.5 3.4 3.8 3.4 3.86 3.6 3.875 3.77 3.5 3.4 3 3.7 3.3 3.4 4 3.56 3.7 78 78 108 78 92 72 60 90 110 60 58 66 72 70 90 145 80 76 82 86 60 68 88 47 82 60 42 70 60 90 60 70 80 80 70 80 60 70 66 70 90 80 80 100 58 65 65 74 68 66 69 63 64 75 60 68 66 62.5 69 62 66 67 65 71 67 68 62 72 66 72 76 70 61 66 73 67 74 69.5 64 62 71 70 62 72 70 62 69 72 3.9 3.75 3.86 4 3.3 3.25 3.9 3.86 3.5 3.8 4.125 3.9 3.4 3.7 3.2 3 3.3 3.6 3.8 3.72 4 4.7 3.5 3.65 3.8 3.56 3.3 3.2 3 3.48 4 3.6 3 3.3 3.4 3.5 3.6 3.95 3.89 3.5 3.84 3.6 3.6 3.9 60 60 80 88 55 78 68 64 76 72 66 66 66 60 74 60 76 66 67 70 90 80 60 120 90 80 40 90 80 80 70 120 80 60 60 70 60 55 47 68 80 68 80 56 62.5 69 75 72 64 67 69 67 63 66 73 74 59 75 71 69 73 65 67 80 65 72 68 65 70 67 71 69 68 68 67 58 66 64 65.5 66 64 60 62 69 67 68 72 63 3.8 3.9 3.3 3.85 3.8 3.7 4 3.5 3.6 4 4 3 3.8 3.95 3.6 4 3.87 3.86 3 3.8 3.3 3 3.75 3.4 3.5 3.97 3 4 3.91 3.6 3.23 3.98 3.33 3.8 3.3 3.6 3.8 3.88 3.9 3.2 4 3.6 3.96 4.208 48 56 76 68 76 64 72 68 80 80 56 68 80 48 80 96 52 76 80 76 80 80 76 100 64 88 80 76 72 80 40 68 92 48 70 80 65 64 48 51 84 74 63 59 68 63 72 68 72 69 65 66 70 64 66 62 60 63 72 68 65 69 70 63 75 67 72 66 75 66 67 63 64 71 71 72 69 71 71 69 66 76 74 72 74 67 72 63 3.65 3.98 3 3.95 3.5 3.8 3.3 3.75 3.6 3.7 3.5 4 3.8 3.2 3.5 3.6 3.98 3.5 3.87 3.71 4 3.2 3 3.4 3.75 3.82 3.3 4 3.9 3.89 3.6 3.7 3.86 4 4 3.5 4.2 3.85 2.65 3.9 3.68 3.6 3.95 3.7 70 65 100 68 76 60 80 82 55 60 66 60 64 82 44 78 52 68 100 75 66 62 60 64 80 90 7 66 60 56 90 70 90 80 70 7 60 60 70 100 80 60 60 80 68 74 61 71 68 64 62 73 69 70 66 67 64 68 71 68 64 72 74 65 71 74 72 64 70 68 66 70 64 68 63.5 65 66 68 66 70 68 63 75 68.5 57 69 65 72 3.75 3.1 3.89 3.6 3.86 3.9 3.8 3.05 3.75 3.58 3.8 3.15 3.46 3.7 3.66 3.24 3.85 3.5 3.3 3.3 3.4 3.6 3.05 3.4 3.7 3.4 3.1 3 4 4 3.45 3.6 4 3.2 4 3.5 3.8 3.8 3.2 4 4 4.15 3.8 3.96 50 60 50 80 60 80 70 80 60 67 2.3 56 74 96 64 64 60 64 120 120 80 80 68 80 50 64 90 72 72 51 76 72 79 82 80 76 10 56 66 72 65 90 58 70 65 66 77 70.5 73 74 72 68 66 4 3.83 2.9 4.1 3.9 3 3.6 3.65 3.7 62 62 70 58 70 78 80 64 110 STA 100 SSI 2019 R Homework 2 - Due Friday, July 12th by 5pm. Book homework is for practice. 1 Book Homework 1. For a standard normal random variable (i.e, for a Z ∼ N (µ = 0, σ = 1) find the following: (a) P (Z < 1.2) (b) P (Z > −2.3) (c) P (−1 < Z < 0.31) (d) The 97.5th percentile. 2. Assume that heart rate (in beats per minute, or bpm) for STA 100 students is distributed normal, with a mean of 110 bpm and a standard deviation of 20.2 bpm. Assume all students in the following problem are selected from this population. (a) Find the probability that a randomly selected students heart rate is above 125. (b) What percentage of randomly selected students could we expect to have a heart rate between 90 and 130? (c) What is the first and third quartile of heartrates for randomly selected students? (d) What is the 8th percentile for heart rates among randomly selected students? 3. The heights of men in a certain population follow a normal distribution with mean 69.7 inches and standard deviation 2.8 inches. (a) If 10 men are selected at random, what is the probability their average height is above 72 inches? (b) If exactly one man is selected at random, what is the probability his average height is above 72 inches? (c) What is the 80th percentile for the average height of 10 men? (d) What is the probability the average height of 10 men is between 70 and 71 inches? 4. Over 9 months, a random sample of 100 women were asked to record their average menstrual cycle length (in days). The sample average was 28.86 days, with a sample standard deviation of 4.24 days. (a) Calculate the 90% confidence interval for the true average menstrual cycle length. (b) Interpret the confidence interval found in (a) in terms of the problem. (c) A researcher hypothesized that womens menstrual cycles are typically the same length as a lunar month - 29.5 days. Does your interval from (a) support this hypothesis? Explain. (d) List two hypothetical ways we could reduce the width of this confidence interval. 5. Continue with the data from Problem 4. (a) If we wanted our confidence interval to have a margin of error of 0.5 days at 90% confidence, how many women should we sample (at least)? (b) If we wanted our confidence interval to have a margin of error of 0.1 days at 90% confidence, how many women should we sample (at least)? (c) What tends to happen to the sample size we need as the margin of error decreases? Explain based on (a) to (b), or in plain English. (d) What tends to happen to the sample size we need as the standard deviation increases? Explain. 1 6. Two treatment costs for a particular medical issue are being compared. The average cost of 210 randomly selected subjects for treatment A was $490, with a standard deviation of $32. The average cost for 180 randomly selected subjects for treatment B was $500, with standard deviation $48. Assume the d.f = 300. (a) Find the 99% confidence interval for the difference costs. (b) Interpret your interval from (a) in terms of the problem. (c) Does your interval suggest that the costs are different? Explain. (d) If we increased the confidence level (i.e, (1 − α)100%), would the new interval be wider or narrower than that found in (a)? Explain (you do not need to calculate the interval). 7. Two baby-food manufacturers are competing, and manufacturer of brand A believes that their brand causes more weight gain in infants than manufacturer of brand B. A sample of size 15 fed their babies brand A for two months, and saw an average weight gain of 36.93 ounces, with a standard deviation of 4.23 ounces. A sample of size 25 fed their babies brand B and saw an average weight gain of 31.36 ounces with a standard deviation of 3.35 ounces. Assume the d.f. = 24. (a) Create a 95% confidence interval for the difference in weight gain between the two baby food brands. (b) Interpret your interval from (a) in terms of the problem. (c) Does your interval suggest one brand of baby food causes more weight gain than the other? Explain. (d) If the sample sizes increased to 100, but everything else remained constant, would our interval widen or narrow? Explain. 2 R Homework Due electronically, on Friday, July 12th by 5pm. I. On Canvas you will find the file student.csv. It contains information on 1548 introduction to statistics students, and has the following columns: Column 1: height: The height of the student. Column 2: hsGPA: The high school GPA of the student. Column 3: pulse: The pulse rate of the student when measured in class. (a) Find the mean, and standard deviation of the column height in this dataset. (b) Use (a) to find the proportion of observations within 2 standard deviation of the mean. Print this proportion. Based on your result, does this suggest students heights are approximately normally distributed? Explain. (c) Plot a QQ plot (normal probability plot). Does this suggest students heights are approximately normally distributed? Explain. (d) Using R, find the 95% confidence interval for the average students height, and report it. II. Use the data from Problem I. (a) Plot a histogram of the column hsGPA. Does this data appear to be normally distributed? Explain. (b) Using R, find the 90% confidence interval for the average students high school GPA, and report it. (c) Interpret your interval from (b) in terms of the problem. (d) Did you need to assume that students high school GPA was normally distributed for your confidence interval to be valid? Explain why or why not. III. You will be using the dataset Radish.csv, which contains the growth rate of radish plants two weeks after germination. The first column is the height of the plants (in cm). The second column is the treatment group, which was either given no fertilizer (the control group) or given fertilizer (the treatment group). Assume the radishes were sampled randomly and independently. (a) Find the 95% confidence interval for this data, and interpret it in terms of the problem. (b) The fertilizer manufacturer claims that by using their fertilizer, plants will grow 1cm more on average than if you use no fertilizer. Does your confidence interval support this claim? Explain. (c) What is the largest difference in growth you could expect with 95% confidence, based on your confidence interval? Be specific about which difference you are looking at. 3 Height 3.4 4.4 3.5 2.9 2.7 2.6 3.7 2.7 2.3 2 1.8 2.3 2.4 2.5 1.6 2.9 2.3 2.8 2.5 2.3 1.6 1.6 3 2.3 3.2 2 2.6 2.4 2.8 1.9 3.6 1.2 2.4 2.2 3.6 1.2 0.9 1.5 2.4 1.7 1.4 1.8 1.9 Treatment Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Control Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized 2.7 2.3 1.8 2.7 2.6 1.3 3 1.4 1.2 2.6 1.8 1.7 1.5 Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized Fertilized
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