CHAPTER 13 Big (or Very Large) Data Project 697 sequence appear to be “random noise” or will it be identified as a pattern that is not random? Also, construct the image represented by the digits and identify it. 001110000111000001000 111111100111000011100 001110001000101000010 10000101000010 Big (or Very Large) Data Project Data Set 25 “Tornadoes” in Appendix B includes lengths (miles) and widths (yards) of 63,160 tornadoes. Use rank correlation to test for an association between those two variables. FROM DATA TO DECISION Critical Thinking: Was the draft lottery random? On December 1, 1969, during the Vietnam War, a lottery was used to determine who would be drafted into the U.S. Army, but the lottery generated considerable controversy. The different dates in a year were placed in 366 individual capsules. First, the 31 January capsules were placed in a box; then the 29 February capsules were added and the two months were mixed. Next, 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 September 14, so men born on that date were drafted first. The accompanying list shows the 366 priority dates in the order of selection. These data are available in Appendix B Data Set 43 “Draft Lottery.” 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. Then plot those 12 means on a graph. (The horizontal scale lists the 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 parts (a), (b), and (c), decide whether this particular draft lottery was fair. Write a statement explaining why you believe that it was or was not fair. If you decided that this lottery was unfair, describe a process for selecting lottery numbers that would have been fair. Day Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec. 1 305 86 108 32 330 249 93 111 225 359 19 129 2 159 144 29 271 298 228 350 45 161 125 34 328 3 251 297 267 83 40 301 115 261 49 244 348 157 4 215 210 275 81 276 20 279 145 232 202 266 165 5 101 214 293 269 364 28 188 54 82 24 310 56 6 224 347 139 253 155 110 327 114 6 87 76 10 7 306 91 122 147 35 85 50 168 8 234 51 12 8 199 181 213 312 321 366 13 48 184 283 97 105 9 194 338 317 219 197 335 277 106 263 342 80 43 10 325 216 323 218 65 206 284 21 71 220 282 41 11 329 150 136 14 37 134 248 324 158 237 46 39 12 221 68 300 346 133 272 15 142 242 72 66 314 13 318 152 259 124 295 69 42 307 175 138 126 163 14 238 4 354 231 178 356 331 198 1 294 127 26 continued
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