Use your sample of states drawn with probability proportional to population, from Exercise 9, for this problem. a Using the sample, estimate the total number of counties in the United States, and find the standard error of your estimate. How does your estimate compare with the true value of total number of counties (which you can calculate, since the file statepps.dat contains the data for the whole population)? b Now suppose that your friend Tom finds the ten values of numbers of counties in your sample, but does not know that you selected these states with probabilities proportional to population. Tom then estimates the total number of counties using formulas for an SRS. What values for the estimated total and its standard error are calculated by Tom? How do these values differ from yours? Is Tom's estimator unbiased for the population total? state, counties, cumcount, landarea, cumland, popn, cumpopn Alabama, 67,67,50750,50750,4137511,4137511 Alaska, 25, 92,570374,621124,587766,4725277 Arizona, 15,107,113642,734766,3832368,8557645 Arkansas, 75,182,52075,786841,2394253,10951898 California, 58,240,155973,942814,30895356,41847254 Colorado, 63,303,103729,1046543, 3464675,45311929 Connecticut,8,311,4845,1051388,3279116, 48591045 Delaware, 3,314,1955,1053343,690884,49281929 District of Columbia,1,315,61,1053404,585221,49867150 Florida, 67,382,53937,1107341,13482716,63349866 Georgia, 159,541,57919,1165260,6773364,70123230 Hawaii, 5,546,6423,1171683,1155726,71278956 Idaho, 44,590,82751,1254434,1065885,72344841 Illinois, 102,692,55593,1310027,11612906,83957747 Indiana, 92,784,35870,1345897,5658323,89616070 Iowa, 99,883,55875,1401772,2802944,92419014 Kansas, 105,988,81823,1483595,2515320,94934334 Kentucky, 120,1108,39732,1523327,3753836, 98688170 Louisiana, 64,1172,43566,1566893,4278889,102967059 Maine, 16,1188,30865,1597758,1236348,104203407 Maryland, 24,1212,9775,1607533,4917269,109120676 Massachusetts, 14,1226,7838,1615371,5992712,115113388 Michigan, 83,1309,56809,1672180,9433665,124547053 Minnesota, 87,1396,79617,1751797,4468165,129015218 Mississippi, 82,1478,46914,1798711,2615208,131630426 Missouri, l15,1593,68898,1867609,5190719,136821145 Montana, 57,1650,145556,2013165, 822347,137643492 Nebraska, 93,1743,76878,2090043,1600524,139244016 Nevada, 18,1761,109806,2199849,1336000,140580016 New Hampshire, 10,1771,8969,2208818,1115087, 141695103 New Jersey,21,1792,7419,2216237,7820260,149515363 New Mexico,33,1825,121365,2337602,1581830,151097193 New York, 62,1887,47224,2384826,18109491,169206684 North Carolina, 100,1987,48718,2433544,6836333,176043017 North Dakota, 53,2040,68994,2502538,634031,176677048 Ohio, 88,2128,40953,2543491,11021419,187698467 Oklahoma, 77,2205,68679,2612170,3205234,190903701 Oregon, 36,2241,96003,2708173,2971567,193875268 Pennsylvania,67,2308,44820,2752993,11995405, 205870673 Rhode Island, 5,2313,1045,2754038,1001344,206872017 South Carolina, 46,2359,30111,2784149,3602854,210474871 South Dakota, 66,2425,75896,2860045,708411,211183282 Tennessee, 95,2520, 41220,2901265,5025261,216208543 Texas, 254,2774,261914, 3163179,17682538,233891081 Utah, 29,2803,82168,3245347,1811215,235702296 Vermont, 14,2817,9249,3254596,571334,236273630 Virginia, 136,2953,39598,3294194,6394481,242668111 Washington,39,2992,66581,3360775,5142746,247810857 West Virginia, 55,3047,24087,3384862,1808860,249619717 Wisconsin, 72,3119,54314,3439176,4992664, 254612381 Wyoming, 23,3142,97105,3536281, 464736,255077117