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. Four measurements were made on two species of flea beetles (Lubischew, 1962). The variables were: y = distance of transverse groove from posterior border of prothorax (um) y2 = length of elytra (in 0.01mm) Y3 = length of second antennal joint (um) 74 = length of third antennal joint (um) The data are given in the following Table 5.5. [4 pts] a) Test Ho: H, = H, using T2. Report and comment on your p-value. b) If the T2-test in part (a) rejects Ho, carry out a t-test on each variable. c) Calculate the discriminant function coefficient vector a = Soll - y2). [4 pts] [2 pts] 301 Table 5.5. Four Measurements on Two Species of Flea Beetles Haltica oleracea Haltica carduorum Experiment Experiment Number Y2 Number Y2 1 189 245 137 163 1 181 305 2 192 260 132 217 2 158 237 3 217 276 141 192 3 184 300 4 221 299 142 213 4 171 273 5 171 239 128 158 5 181 297 6 192 262 147 173 6 181 308 7 213 278 136 201 7 177 8 192 255 128 185 8 198 308 9 170 244 128 192 9 180 286 10 201 276 146 186 10 177 299 11 195 242 128 192 176 317 12 205 263 147 192 192 312 13 180 252 121 167 285 14 192 283 138 183 14 169 287 15 200 294 138 188 15 164 265 16 192 277 150 177 16 181 308 17 200 287 136 173 17 192 276 18 181 255 146 183 18 181 278 19 192 287 141 198 19 175 271 20 197 303 184 133 166 162 163 160 166 141 146 171 166 166 141 162 147 157 154 149 140 170 209 188 231 213 224 223 221 197 214 192 213 209 200 214 192 204 209 235 192 205 12 13 176