2) The data file counties.csv contains information on land area, population, number of physicians, unemployment, and a number of other quantities for an SRS of 100 of the 3141 counties in the United States (U.S. Census Bureau, 1994). The total land area for the United States is 3,536,278 square miles; 1993 population was estimated to be 255,077,536. a) Draw a histogram of the farm populations (the variable “farmpop") for the 100 counties. Comment on the shape of the distribution. b) Estimate the total farm population in the United States, along with its standard error, using Nỹ. c) Plot the farm populations vs. land areas (variables “farmpop” and “landarea”) for each county, and find the sample correlation coefficient between them. Which method do you think is more appropriate for these data: ratio estimation or regression estimation or none of them? d) Using ratio estimation, use the auxiliary variable land area to estimate the total farm population in the United States, along with the standard error. e) The “true” value for total farm population is 3,871,583. Which method of estimation came closer: SRS or ratio estimation? Here is the baseball.csv data. A B 1 RN State 2 27 AL 3 48 AL C County Escambia Marshall D E F G H L M N P Q R S landarea totpop physician enroll percpub civlabor unemp 948 36023 24 567 73524 44 6931 11928 95.4 15247 1339 531 414 farmpop numfarm farmacre fedgrant fedciv 90646 122.3 milit veterans percviet 85 370 3723 27.1 98.6 38803 3189 1592 1582 136599 235.7 316 748 8510 29.1 4 85 AK Prince of 7325 6408 7 1317 98.6 2787 383 71 2 214 32.2 126 63 809 44.6 5 126 AR Cross 616 19261 11 4066 99.1 8336 704 762 492 339830 81.4 87 107 1505 23.9 6 158 AR Newton 7 186 CA Butte 823 1640 188377 7649 3 1579 99.2 3280 270 600 562 98106 31.7 71 44 807 25.5 327 27899 94.5 77500 7303 2818 2030 494530 688 570 577 23958 27.6 8 254 CO Custer 9 286 CO 10 305 CT Ouray Hartford 739 542 736 847009 2140 1 364 97.5 789 42 145 2497 3 429 99.3 1919 109 112 2851 11 340 FL Hardee 637 20084 12 350 FL Lake 953 161228 13 371 FL St. Lucie 573 161106 14 422 GA Crisp 274 20377 15 432 GA Echols 16 527 GA Walton 17 559 ID 18 586 ID 404 329 40750 Camas 1075 755 Shoshone 2634 13644 2291 ུ རྞྞ ༦ ༤༠ ° གླ° 128982 90 470164 32673 623 130 88 656 60277 150334 -99 7 11 10 347 37.8 5.7 5 11 337 35.9 4051.1 8504 2975 93683 24.9 11 167 3802 19777 99.1 91.5 58285 9368 987 1202 1130 303892 60.6 55 44 2071 21.4 5182 1582 1285 232657 664.2 499 403 26923 21.6 176 22769 90.6 65078 8966 257 522 297433 543.7 536 348 23205 21.1 20 4112 95.1 8980 573 341 192 112431 67.3 64 170 1893 32.3 483 100 875 39 162 80 13745 4.8 5 19 242 30.2 29 7210 95.2 17404 955 756 469 65220 96.2 93 307 3551 28.4 0 147 100 365 24 66 117 174842 5.9 21 0 82 32.9 9 2683 97.8 5041 981 29 46 5148 59.5 203 75 2070 29.3 19 606 IL 20 617 IL Cook Ford 946 5139341 486 13914 15153 11 853115 81.5 2715405 196796 196 389 46907 20151.2 61976 16480 457880 24.2 2555 97.6 7265 481 1477 729 297013 54.4 69 40 1741 32.2 21 630 IL Jasper 494 10519 3 1994 91.7 5828 434 2795 894 262198 31.3 52 31 1073 22.7 22 639 IL Lake 23 698 IN 24 702 IN Boone Clark 25 703 IN Clay 26 743 IN 27 780 IN Martin Washingt 448 541047 423 38381 375 89658 358 25078 336 515 24398 1093 88975 88.9 319950 14863 586 448 82349 1641.8 9399 21454 53060 32.7 81 7062 95.1 21157 716 2258 822 227524 83.6 111 213 4283 29.5 109 15779 92.4 47787 3025 1310 691 118810 314.6 2980 488 11222 31.8 11 4506 95.9 10971 748 1811 646 162594 82.9 80 137 2874 22.2 10510 4 1923 95.2 5353 374 695 9 4443 99.1 11411 882 2119 361 67373 1034 195118 244.9 5240 109 1359 31.2 63.4 69 128 2745 29.7 counties + ་|