Hypothesis Testing-Regression. (Partly from Keller and Warrack, 5" Ed.) When setting up their rates policy, Automobile Insurance companies usually take in consideration several factors like age, marital status, vehicle type, profession, and distance driven yearly. To this end one of these companies conducted a survey on a sample of 200 people (100 male and 100 female) to investigate the effect of gender on driving habits. The number of miles driven by each person last year was recorded, as well as the distances of their homes to the Capital. The resulting dataset is stored in the third sheet Data of this Group Work Excel file (MTH203- STA201_Group Work-Fall 2020.xlsx). The variables used are defined as follows: Column 1: Miles Driven (in miles). Column 2: Distance to Capital (in miles). Column 3: Gender Code (1 = male, 2 = female). a. Use appropriate Excel Descriptive Statistics tools to summarize this data (describe Miles Driven and Distance to Capital overall and for each gender separately). b. The company believes that on the average, most people drive more than 10,000 miles per year. On the basis of the entire sample, discuss this issue based on a hypothesis test for the population mean number of miles driven per year at the 5% level of significance. c. On the other hand, the company believes that on the average, the yearly number of miles driven by males is more than that for females. Repeat the test of hypothesis of part (b.), but for each gender separately. Based on the outcomes of these two tests approve or disapprove the company's belief. d. Use a test of hypothesis to check whether there is a significant linear relationship between Miles Driven and Distance to Capital at the 5% then the 1% level of significance. Based on the value of R-Squared (Coefficient of Determination), is the regression of Miles Driven on Distance to Capital a good model? Explain. A B 1 2 Miles Driven Distance to Capital Gender 4000 220.1 9800 5.0 2 3 1 4 11100 2.1 2 5 7.0 2 14100 11300 6 2.5 1 7 10700 1.4 1 8 9.9 2 6200 13000 9 5.3 1 10 8200 4.0 2 11 2.3 2. 8900 11100 12 2.1 1 13 6.6 2 14 97.5 2 2 13800 26100 11700 26000 15 1 3.2 501.3 16 1 17 14800 8.0 1 18 7100 1 7.0 3.7 19 12000 2 20 2.5 1 11300 8700 2.8 1 21 22 7400 6.1 2 23 7100 7.0 1 24 9300 1.5 2 25 8700 2.8 2 26 7.3 2 27 7000 9100 23500 1 1.9 109.3 28 1 29 9400 1.2 1 30 9800 0.4 1 31 14100 7.0 2 32 10100 0.1 1 A B 32 1 10100 9900 0.1 0.2 33 2 2 34 8200 4.0 N 35 10500 2 7200 1 10900 2 36 37 38 39 2. 1 40 1.0 6.7 1.7 4.5 3.3 2.6 99.6 3.3 135.8 4.3 3.7 2 41 2 2 8000 8500 11400 6300 8500 7500 12400 12000 8000 9600 8400 10300 2 2 2 4.5 2 0.8 2 3.5 2 0.6 2 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 8600 3.0 1 24.2 2. 3600 39000 13500 1 137.4 6.1 1 3.8 1 12100 8900 13700 2.3 1 6.4 2. 2 6.4 2 58 1.5 1 7300 10800 11400 12500 2.6 1 4.5 2 59 60 61 62 0.1 1 0.2 2 63 2 10000 10100 12900 10400 9500 12300 64 2 5.1 0.8 1.0 411.8 65 2 66 2 A . B 04 10400 0.0 65 1.0 2 411.8 2 66 67 9500 12300 8800 11400 2.6 2 2 68 69 2.6 4.3 12400 1 70 10000 0.1 1 9800 0.4 2 10400 0.8 1 13700 6.4 2 71 72 73 74 75 76 1 1 8100 43000 10200 10000 10500 4.2 40.8 0.3 0.1 1 77 1 78 1.0 2 79 5.8 2 7500 13900 11900 2 80 81 82 2 6.7 3.5 2 99.1 1 83 2 84 2 5500 10200 7600 14100 6800 9700 13500 85 86 1 0.4 5.6 0.7 127.9 0.6 1 1 87 88 89 6.1 2 2 2 7100 7.0 2 7100 7.0 2 90 91 1.4 2 92 4.7 2 10700 12600 25100 11500 7900 160.3 93 94 1 2.8 1 4.8 1 95 96 11400 2.6 2 97 6.6 2 13800 9300 98 1.5 1 99 15100 8.5 2 . B JUU 1 99 15100 8.5 2 11200 2.3 2 100 101 140.4 1 10200 10900 102 2 1.7 409.2 6400 2 103 104 6700 8.2 1 105 0.6 2 10300 10600 11300 1.2 1 2 2.5 106 107 108 109 8600 1 3.0 333.3 2 1.2 1 5.6 1 8500 9400 7600 12300 12400 6400 4.2 110 111 112 113 114 115 1 4.3 2 70.1 1 10600 1.2 1 1 116 117 8500 9500 3.3 381.0 4.5 1 1 118 119 120 8000 15500 9.0 2 9100 1.9 1 14500 7.6 1 121 122 13500 6.1 1 1.7 1 123 124 9200 10100 0.2 1 9800 2 0.4 212.3 2 5600 14200 5100 2 125 126 127 128 129 130 131 132 7.2 145.1 117.9 2 6800 1 3.8 1 2 12100 3700 9900 11600 23.3 0.2 3.0 2 133 2 A B 2 11600 8500 3.0 3.3 2 14.0 1 9200 16100 12500 9.9 1 4.5 2 133 134 135 136 137 138 139 140 141 142 9400 1.2 2 2 6900 10000 8000 12700 7.6 0.1 4.5 1 1 4.8 1 143 13500 1 144 2 10100 9800 5300 145 146 147 6.1 0.2 200.4 313.6 1.7 2 2 9200 1 148 2 2 1 1 149 150 5700 9300 11300 8400 13800 11000 11.8 1.5 2.5 3.5 6.6 1 1 2 1.9 1 10000 1 151 152 153 154 155 156 157 158 21.0 2.1 9000 2 7.6 1 6900 11200 2.3 1 8400 3.5 2 2 13300 10700 9900 5.8 1.4 1 69.2 2 2 8.6 2 159 160 161 162 163 164 165 166 6600 14400 1 0.7 2.8 99.6 8700 6300 2 2. 2 2 7600 75.6 1 167 10300 0.6 1 1 168 6400 9.2 2 . B C IVU 167 10300 0.6 1 168 2. 6400 18000 9.2 12.4 1 3.2 2 2.3 1 3.8 1 11700 8900 12100 5600 14700 8600 9700 2 312.3 7.9 1 1 3.0 0.6 5.3 2 1 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 7700 36000 10200 97.5 1 0.4 2 12600 4.7 1 6800 7.9 1 11100 2.1 2 1 7400 5800 66.1 211.4 1 1 4.0 211.0 1 187 8200 5900 14600 11700 8400 7.8 2 3.2 2 188 189 3.5 2 190 432.5 1 52200 7800 191 2 84.8 411.4 5800 2 192 193 12900 1 5.1 1.7 1 194 195 196 10900 11200 2.3 1 111.9 1 2 197 198 199 9100 3900 2700 10500 93.5 333.2 1.0 2 1 5.3 1 200 201 7700 10100 0.2 1 Hypothesis Testing-Regression. (Partly from Keller and Warrack, 5" Ed.) When setting up their rates policy, Automobile Insurance companies usually take in consideration several factors like age, marital status, vehicle type, profession, and distance driven yearly. To this end one of these companies conducted a survey on a sample of 200 people (100 male and 100 female) to investigate the effect of gender on driving habits. The number of miles driven by each person last year was recorded, as well as the distances of their homes to the Capital. The resulting dataset is stored in the third sheet Data of this Group Work Excel file (MTH203- STA201_Group Work-Fall 2020.xlsx). The variables used are defined as follows: Column 1: Miles Driven (in miles). Column 2: Distance to Capital (in miles). Column 3: Gender Code (1 = male, 2 = female). a. Use appropriate Excel Descriptive Statistics tools to summarize this data (describe Miles Driven and Distance to Capital overall and for each gender separately). b. The company believes that on the average, most people drive more than 10,000 miles per year. On the basis of the entire sample, discuss this issue based on a hypothesis test for the population mean number of miles driven per year at the 5% level of significance. c. On the other hand, the company believes that on the average, the yearly number of miles driven by males is more than that for females. Repeat the test of hypothesis of part (b.), but for each gender separately. Based on the outcomes of these two tests approve or disapprove the company's belief. d. Use a test of hypothesis to check whether there is a significant linear relationship between Miles Driven and Distance to Capital at the 5% then the 1% level of significance. Based on the value of R-Squared (Coefficient of Determination), is the regression of Miles Driven on Distance to Capital a good model? Explain. A B 1 2 Miles Driven Distance to Capital Gender 4000 220.1 9800 5.0 2 3 1 4 11100 2.1 2 5 7.0 2 14100 11300 6 2.5 1 7 10700 1.4 1 8 9.9 2 6200 13000 9 5.3 1 10 8200 4.0 2 11 2.3 2. 8900 11100 12 2.1 1 13 6.6 2 14 97.5 2 2 13800 26100 11700 26000 15 1 3.2 501.3 16 1 17 14800 8.0 1 18 7100 1 7.0 3.7 19 12000 2 20 2.5 1 11300 8700 2.8 1 21 22 7400 6.1 2 23 7100 7.0 1 24 9300 1.5 2 25 8700 2.8 2 26 7.3 2 27 7000 9100 23500 1 1.9 109.3 28 1 29 9400 1.2 1 30 9800 0.4 1 31 14100 7.0 2 32 10100 0.1 1 A B 32 1 10100 9900 0.1 0.2 33 2 2 34 8200 4.0 N 35 10500 2 7200 1 10900 2 36 37 38 39 2. 1 40 1.0 6.7 1.7 4.5 3.3 2.6 99.6 3.3 135.8 4.3 3.7 2 41 2 2 8000 8500 11400 6300 8500 7500 12400 12000 8000 9600 8400 10300 2 2 2 4.5 2 0.8 2 3.5 2 0.6 2 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 8600 3.0 1 24.2 2. 3600 39000 13500 1 137.4 6.1 1 3.8 1 12100 8900 13700 2.3 1 6.4 2. 2 6.4 2 58 1.5 1 7300 10800 11400 12500 2.6 1 4.5 2 59 60 61 62 0.1 1 0.2 2 63 2 10000 10100 12900 10400 9500 12300 64 2 5.1 0.8 1.0 411.8 65 2 66 2 A . B 04 10400 0.0 65 1.0 2 411.8 2 66 67 9500 12300 8800 11400 2.6 2 2 68 69 2.6 4.3 12400 1 70 10000 0.1 1 9800 0.4 2 10400 0.8 1 13700 6.4 2 71 72 73 74 75 76 1 1 8100 43000 10200 10000 10500 4.2 40.8 0.3 0.1 1 77 1 78 1.0 2 79 5.8 2 7500 13900 11900 2 80 81 82 2 6.7 3.5 2 99.1 1 83 2 84 2 5500 10200 7600 14100 6800 9700 13500 85 86 1 0.4 5.6 0.7 127.9 0.6 1 1 87 88 89 6.1 2 2 2 7100 7.0 2 7100 7.0 2 90 91 1.4 2 92 4.7 2 10700 12600 25100 11500 7900 160.3 93 94 1 2.8 1 4.8 1 95 96 11400 2.6 2 97 6.6 2 13800 9300 98 1.5 1 99 15100 8.5 2 . B JUU 1 99 15100 8.5 2 11200 2.3 2 100 101 140.4 1 10200 10900 102 2 1.7 409.2 6400 2 103 104 6700 8.2 1 105 0.6 2 10300 10600 11300 1.2 1 2 2.5 106 107 108 109 8600 1 3.0 333.3 2 1.2 1 5.6 1 8500 9400 7600 12300 12400 6400 4.2 110 111 112 113 114 115 1 4.3 2 70.1 1 10600 1.2 1 1 116 117 8500 9500 3.3 381.0 4.5 1 1 118 119 120 8000 15500 9.0 2 9100 1.9 1 14500 7.6 1 121 122 13500 6.1 1 1.7 1 123 124 9200 10100 0.2 1 9800 2 0.4 212.3 2 5600 14200 5100 2 125 126 127 128 129 130 131 132 7.2 145.1 117.9 2 6800 1 3.8 1 2 12100 3700 9900 11600 23.3 0.2 3.0 2 133 2 A B 2 11600 8500 3.0 3.3 2 14.0 1 9200 16100 12500 9.9 1 4.5 2 133 134 135 136 137 138 139 140 141 142 9400 1.2 2 2 6900 10000 8000 12700 7.6 0.1 4.5 1 1 4.8 1 143 13500 1 144 2 10100 9800 5300 145 146 147 6.1 0.2 200.4 313.6 1.7 2 2 9200 1 148 2 2 1 1 149 150 5700 9300 11300 8400 13800 11000 11.8 1.5 2.5 3.5 6.6 1 1 2 1.9 1 10000 1 151 152 153 154 155 156 157 158 21.0 2.1 9000 2 7.6 1 6900 11200 2.3 1 8400 3.5 2 2 13300 10700 9900 5.8 1.4 1 69.2 2 2 8.6 2 159 160 161 162 163 164 165 166 6600 14400 1 0.7 2.8 99.6 8700 6300 2 2. 2 2 7600 75.6 1 167 10300 0.6 1 1 168 6400 9.2 2 . B C IVU 167 10300 0.6 1 168 2. 6400 18000 9.2 12.4 1 3.2 2 2.3 1 3.8 1 11700 8900 12100 5600 14700 8600 9700 2 312.3 7.9 1 1 3.0 0.6 5.3 2 1 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 7700 36000 10200 97.5 1 0.4 2 12600 4.7 1 6800 7.9 1 11100 2.1 2 1 7400 5800 66.1 211.4 1 1 4.0 211.0 1 187 8200 5900 14600 11700 8400 7.8 2 3.2 2 188 189 3.5 2 190 432.5 1 52200 7800 191 2 84.8 411.4 5800 2 192 193 12900 1 5.1 1.7 1 194 195 196 10900 11200 2.3 1 111.9 1 2 197 198 199 9100 3900 2700 10500 93.5 333.2 1.0 2 1 5.3 1 200 201 7700 10100 0.2 1