Discussion:
Q: In 1970, a lottery was used to determine who would be drafted into the U.S. Army. The 366 dates in the year were placed in individual capsules. First , the 31 Jan. capsules were placed in a box; then the 29 Feb. capsules were added and the two months were mixed. Then the 31 March capsules were added and the three months were mixed. This process continued until all months were included. The first capsule selected was Sept. 14, so men born on that date were drafted first. The accompanying spreadsheet shows the 366 dates in the order of selection.
ANALYZING THE RESULTS
a. Use the runs test to test the sequence for randomness above and below the median of 183.5.
b. Use the Kruskal-Wallis test to test the claim that the 12 months had priority numbers drawn from the same population.
c. Calculate the 12 monthly means. (The horizontal scale list 12 months, and the vertical scale ranges from 100 to 260) Note any pattern suggesting that the original priority numbers were not randomly selected.
d. Based on the results from a, b, and c, was this lottery fair?
| 305 |
Jan |
| 159 |
Jan |
| 251 |
Jan |
| 215 |
Jan |
| 101 |
Jan |
| 224 |
Jan |
| 306 |
Jan |
| 199 |
Jan |
| 194 |
Jan |
| 325 |
Jan |
| 329 |
Jan |
| 221 |
Jan |
| 318 |
Jan |
| 238 |
Jan |
| 17 |
Jan |
| 121 |
Jan |
| 235 |
Jan |
| 140 |
Jan |
| 58 |
Jan |
| 280 |
Jan |
| 186 |
Jan |
| 337 |
Jan |
| 118 |
Jan |
| 59 |
Jan |
| 52 |
Jan |
| 92 |
Jan |
| 355 |
Jan |
| 77 |
Jan |
| 349 |
Jan |
| 164 |
Jan |
| 211 |
Jan |
| 86 |
Feb |
| 144 |
Feb |
| 297 |
Feb |
| 210 |
Feb |
| 214 |
Feb |
| 347 |
Feb |
| 91 |
Feb |
| 181 |
Feb |
| 338 |
Feb |
| 216 |
Feb |
| 150 |
Feb |
| 68 |
Feb |
| 152 |
Feb |
| 4 |
Feb |
| 89 |
Feb |
| 212 |
Feb |
| 189 |
Feb |
| 292 |
Feb |
| 25 |
Feb |
| 302 |
Feb |
| 363 |
Feb |
| 290 |
Feb |
| 57 |
Feb |
| 236 |
Feb |
| 179 |
Feb |
| 365 |
Feb |
| 205 |
Feb |
| 299 |
Feb |
| 285 |
Feb |
| 108 |
Mar |
| 29 |
Mar |
| 267 |
Mar |
| 275 |
Mar |
| 293 |
Mar |
| 139 |
Mar |
| 122 |
Mar |
| 213 |
Mar |
| 317 |
Mar |
| 323 |
Mar |
| 136 |
Mar |
| 300 |
Mar |
| 259 |
Mar |
| 354 |
Mar |
| 169 |
Mar |
| 166 |
Mar |
| 33 |
Mar |
| 332 |
Mar |
| 200 |
Mar |
| 239 |
Mar |
| 334 |
Mar |
| 265 |
Mar |
| 256 |
Mar |
| 258 |
Mar |
| 343 |
Mar |
| 170 |
Mar |
| 268 |
Mar |
| 223 |
Mar |
| 362 |
Mar |
| 217 |
Mar |
| 30 |
Mar |
| 32 |
Apr |
| 271 |
Apr |
| 83 |
Apr |
| 81 |
Apr |
| 269 |
Apr |
| 253 |
Apr |
| 147 |
Apr |
| 312 |
Apr |
| 219 |
Apr |
| 218 |
Apr |
| 14 |
Apr |
| 346 |
Apr |
| 124 |
Apr |
| 231 |
Apr |
| 273 |
Apr |
| 148 |
Apr |
| 260 |
Apr |
| 90 |
Apr |
| 336 |
Apr |
| 345 |
Apr |
| 62 |
Apr |
| 316 |
Apr |
| 252 |
Apr |
| 2 |
Apr |
| 351 |
Apr |
| 340 |
Apr |
| 74 |
Apr |
| 262 |
Apr |
| 191 |
Apr |
| 208 |
Apr |
| 330 |
May |
| 298 |
May |
| 40 |
May |
| 276 |
May |
| 364 |
May |
| 155 |
May |
| 35 |
May |
| 321 |
May |
| 197 |
May |
| 65 |
May |
| 37 |
May |
| 133 |
May |
| 295 |
May |
| 178 |
May |
| 130 |
May |
| 55 |
May |
| 112 |
May |
| 278 |
May |
| 75 |
May |
| 183 |
May |
| 250 |
May |
| 326 |
May |
| 319 |
May |
| 31 |
May |
| 361 |
May |
| 357 |
May |
| 296 |
May |
| 308 |
May |
| 226 |
May |
| 103 |
May |
| 313 |
May |
| 249 |
Jun |
| 228 |
Jun |
| 301 |
Jun |
| 20 |
Jun |
| 28 |
Jun |
| 110 |
Jun |
| 85 |
Jun |
| 366 |
Jun |
| 335 |
Jun |
| 206 |
Jun |
| 134 |
Jun |
| 272 |
Jun |
| 69 |
Jun |
| 356 |
Jun |
| 180 |
Jun |
| 274 |
Jun |
| 73 |
Jun |
| 341 |
Jun |
| 104 |
Jun |
| 360 |
Jun |
| 60 |
Jun |
| 247 |
Jun |
| 109 |
Jun |
| 358 |
Jun |
| 137 |
Jun |
| 22 |
Jun |
| 64 |
Jun |
| 222 |
Jun |
| 353 |
Jun |
| 209 |
Jun |
| 93 |
Jul |
| 350 |
Jul |
| 115 |
Jul |
| 279 |
Jul |
| 188 |
Jul |
| 327 |
Jul |
| 50 |
Jul |
| 13 |
Jul |
| 277 |
Jul |
| 284 |
Jul |
| 248 |
Jul |
| 15 |
Jul |
| 42 |
Jul |
| 331 |
Jul |
| 322 |
Jul |
| 120 |
Jul |
| 98 |
Jul |
| 190 |
Jul |
| 227 |
Jul |
| 187 |
Jul |
| 27 |
Jul |
| 153 |
Jul |
| 172 |
Jul |
| 23 |
Jul |
| 67 |
Jul |
| 303 |
Jul |
| 289 |
Jul |
| 88 |
Jul |
| 270 |
Jul |
| 287 |
Jul |
| 193 |
Jul |
| 111 |
Aug |
| 45 |
Aug |
| 261 |
Aug |
| 145 |
Aug |
| 54 |
Aug |
| 114 |
Aug |
| 168 |
Aug |
| 48 |
Aug |
| 106 |
Aug |
| 21 |
Aug |
| 324 |
Aug |
| 142 |
Aug |
| 307 |
Aug |
| 198 |
Aug |
| 102 |
Aug |
| 44 |
Aug |
| 154 |
Aug |
| 141 |
Aug |
| 311 |
Aug |
| 344 |
Aug |
| 291 |
Aug |
| 339 |
Aug |
| 116 |
Aug |
| 36 |
Aug |
| 286 |
Aug |
| 245 |
Aug |
| 352 |
Aug |
| 167 |
Aug |
| 61 |
Aug |
| 333 |
Aug |
| 11 |
Aug |
| 225 |
Sep |
| 161 |
Sep |
| 49 |
Sep |
| 232 |
Sep |
| 82 |
Sep |
| 6 |
Sep |
| 8 |
Sep |
| 184 |
Sep |
| 263 |
Sep |
| 71 |
Sep |
| 158 |
Sep |
| 242 |
Sep |
| 175 |
Sep |
| 1 |
Sep |
| 113 |
Sep |
| 207 |
Sep |
| 255 |
Sep |
| 246 |
Sep |
| 177 |
Sep |
| 63 |
Sep |
| 204 |
Sep |
| 160 |
Sep |
| 119 |
Sep |
| 195 |
Sep |
| 149 |
Sep |
| 18 |
Sep |
| 233 |
Sep |
| 257 |
Sep |
| 151 |
Sep |
| 315 |
Sep |
| 359 |
Oct |
| 125 |
Oct |
| 244 |
Oct |
| 202 |
Oct |
| 24 |
Oct |
| 87 |
Oct |
| 234 |
Oct |
| 283 |
Oct |
| 342 |
Oct |
| 220 |
Oct |
| 237 |
Oct |
| 72 |
Oct |
| 138 |
Oct |
| 294 |
Oct |
| 171 |
Oct |
| 254 |
Oct |
| 288 |
Oct |
| 5 |
Oct |
| 241 |
Oct |
| 192 |
Oct |
| 243 |
Oct |
| 117 |
Oct |
| 201 |
Oct |
| 196 |
Oct |
| 176 |
Oct |
| 7 |
Oct |
| 264 |
Oct |
| 94 |
Oct |
| 229 |
Oct |
| 38 |
Oct |
| 79 |
Oct |
| 19 |
Nov |
| 34 |
Nov |
| 348 |
Nov |
| 266 |
Nov |
| 310 |
Nov |
| 76 |
Nov |
| 51 |
Nov |
| 97 |
Nov |
| 80 |
Nov |
| 282 |
Nov |
| 46 |
Nov |
| 66 |
Nov |
| 126 |
Nov |
| 127 |
Nov |
| 131 |
Nov |
| 107 |
Nov |
| 143 |
Nov |
| 146 |
Nov |
| 203 |
Nov |
| 185 |
Nov |
| 156 |
Nov |
| 9 |
Nov |
| 182 |
Nov |
| 230 |
Nov |
| 132 |
Nov |
| 309 |
Nov |
| 47 |
Nov |
| 281 |
Nov |
| 99 |
Nov |
| 174 |
Nov |
| 129 |
Dec |
| 328 |
Dec |
| 157 |
Dec |
| 165 |
Dec |
| 56 |
Dec |
| 10 |
Dec |
| 12 |
Dec |
| 105 |
Dec |
| 43 |
Dec |
| 41 |
Dec |
| 39 |
Dec |
| 314 |
Dec |
| 163 |
Dec |
| 26 |
Dec |
| 320 |
Dec |
| 96 |
Dec |
| 304 |
Dec |
| 128 |
Dec |
| 240 |
Dec |
| 135 |
Dec |
| 70 |
Dec |
| 53 |
Dec |
| 162 |
Dec |
| 95 |
Dec |
| 84 |
Dec |
| 173 |
Dec |
| 78 |
Dec |
| 123 |
Dec |
| 16 |
Dec |
| 3 |
Dec |
| 100 |
Dec |