4) Baseball Data: a) Using the teams as psus (N = with equal 30), draw a one-stage cluster sample of 6 teams (n = 6) probabilities. Your sample should have approximately 150 players altogether. b) Use your sample to estimate the mean of logsal = log(salary) along with its SE. Hint: Create a new dataset with an additional column for logsal. If samo is your sample, then saml = data.frame (sam0, logsal=log (sam0$ salary)) Here is the data A B C D E F G H J K L M N о P Q R S T U V W X Y AA AB AC AD AE AF team leagueID player salary POS G GS InnOuts PO A E DP PB GB AB R H SecB ThiB HR RBI SB CS BB SO IBB HBP SH SF GIDP pitcher 2 ANA AL anderga0 6200000 CF 112 3 ANA AL colonba0 1.1E+07 P 4 ANA AL davanjeO 375000 CF 108 5 ANA AL donnebro 375000 P 6 ANA AL eckstda0 7 ANA AL erstada0 8 ANA AL 2150000 SS 7750000 1B escobke0 5750000 P 142 125 9 ANA AL figgicho 320000 3B 148 10 ANA AL glaustro 9900000 3B 11 ANA AL greggke0 301500 P 12 ANA AL guerrvl0 1.1E+07 RF 156 13 ANA 14 ANA AL AL guilljoo 2200000 LF 148 haltesho 575000 3B 15 ANA AL 16 ANA AL kenneado 2500000 2B lackejo0 375000 P 144 17 ANA AL molinbe0 2025000 C 18 ANA AL molinjo0 335000 C 19 ANA AL ortizra0 20 ANA AL pauljo01 3266667 P 335000 C 21 ANA AL percitro 7833333 P 22 ANA AL rodrifro 375000 P 23 ANA AL salmotio 24 ANA AL seleaa01 9900000 RF 8666667 P 25 ANA AL shielsc0 375000 P 26 ANA AL washbja0 5450000 P 27 ANA AL weberbe0 900000 P 28 ARI NL alomaro0 1000000 2B 29 ARI NL baergca0 1000000 1B 30 ARI 31 ARI NL bautidao 4000000 RF NL choatra0 325750 P 32 ARI NL cintralo 335000 SS 33 ARI NL colbrgro 2750000 1B 34 ARI NL daiglca0 300000 P 35 ARI NL desseel0 4000000 P 36 ARI NL ADI estalbo0 baseball 550000 C ༄^8༞¥8ཨྠཧྨ^ 8ཨྠ¥ཝཱ"b " " ྴ "ng - nn༅%ę¥818E 8" 3 5 136 124 1 58 5 143 135 46 2 97 1 46 3 3 60 3 3 38 79 141 69 154 20 11 36 8#h°⌘ཟླ⌘⌘9°⌘d⌘ལྐ⌘h!༠༠༠༠ཟླ°༢°ཀླསྒྱུg °⌘--༠ 92 2375 211 34 625 27 743 0 126 3575 3196 986 33 625 80 2116 19 495 0 263 3702 3471 22 640 138 3675 32 595 2286 57 1573 14 384 16 504 0 149 0 252 5 117 24 396 0 316 25 448 0 67 23 610 4 135 107 3536 0 152 ་ྒུ༩མྦྷཝ༔༤༦=ས ༔ ༔ 8 ཧྨ ཎྷེ ་ྒུ ཙྩུ ཎྜ ༞ ཤྩ ༠ ༠ ąསྙ༠ ཉྩཱ 5 2 1 NA 112 442 57 133 20 1 14 75 2 1 29 75 8 30 3 4 NA 3 3 0 0 0 0 0 0 0 0 0 75 1 0 1 NA 108 285 41 79 11 4 7 34 18 3 46 2 2 0 Ο ΝΑ 5 0 0 0 0 0 0 0 0 0 0 198 309 6 75 NA 142 566 92 156 24 1 2 35 16 5 42 49 66 4 83 NA 125 495 79 146 29 1 7 69 16 1 37 16 24 0 1 NA 1 2 0 0 0 0 0 0 0 0 0 57 129 11 9 NA 148 577 83 171 22 17 5 60 34 13 49 11 27 2 2 NA 58 207 47 52 11 1 18 42 2 3 31 2 5 0 1 NA 5 0 0 0 0 0 0 0 0 0 0 308 13 9 2 NA 156 612 124 206 39 2 39 126 15 3 52 266 9 6 1 NA 148 565 88 166 28 3 27 104 5 4 37 26 46 10 2 NA 46 114 10 23 5 0 4 13 1 1 7 255 388 12 71 NA 144 468 70 130 20 5 10 48 15 5 41 15 23 0 1 NA 2 2 0 0 0 0 0 0 0 0 0 597 56 3 5 6 97 337 36 93 13 0 10 54 0 1 18 441 37 3 4 3 73 203 26 53 10 2 3 25 4 1 10 6 13 2 1 NA 1 3 0 0 0 0 0 0 0 0 0 134 9 1 2 2 46 70 11 17 3 0 2 10 2 1 7 1 3 0 Ο ΝΑ 3 0 0 0 0 0 0 0 0 0 0 5 9 0 Ο ΝΑ 3 0 0 0 0 0 0 0 0 0 0 15 1 0 Ο ΝΑ 60 186 15 47 7 0 2 23 1 0 14 gp- ་॰༠!=་ལྟ°!88སྐྱ- ad° °°{¥ 6 1 0 3 3 0 1 0 0 0 0 0 1 54 2 0 1 5 2 0 0 0 0 0 0 0 1 1 13 14 2 11 0 74 1 4 3 4 9 0 0 0 0 0 0 0 1 94 0 0 10 2 6 0 52 3 3 0 1 6 0 0 0 0 0 0 0 1 74 14 8 0 8 19 0 92 5 15 0 3 14 0 30 0 0 0 0 3 0 92 13 9 2 10 0 1 0 0 0 0 0 1 35 1 2 2 4 18 0 52 0 0 5 0 6 0 0 0 0 0 0 1 1 17 0 0 3 1 2 0 0 Ο ΝΑ 0 0 0 1 0 0 0 0 0 0 1 41 0 2 0 4 2 0 3 10 2 2 NA 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 13 1 Ο ΝΑ 3 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 3 22 1 2 NA 3 5 0 2 0 0 0 1 0 0 0 0 0 0 2 0 0 1 0 0 Ο ΝΑ 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 48 53 3 10 NA 38 110 14 34 5 2 3 16 0 2 12 18 0 1 2 0 2 0 32 4 0 2 NA 79 85 6 20 2 0 2 11 0 0 6 12 0 3 0 0 7 0 265 8 4 1 NA 141 539 64 154 27 1 11 65 6 2 35 66 2 4 1 3 20 0 3 10 0 1 NA 69 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 125 3297 141 383 15 61 NA 154 564 56 148 31 7 4 49 3 3 31 59 2 2 12 4 11 0 1 27 7 1 0 Ο ΝΑ 20 27 1 3 0 0 0 1 0 0 1 5 0 0 0 0 0 0 10 147 5 6 0 Ο ΝΑ 11 17 2 2 2 0 0 0 0 0 0 7 0 0 1 0 1 1 9 256 5 12 1 Ο ΝΑ 36 18 0 3 2 0 0 0 0 0 3 3 0 0 4 0 1 1 Insassa er 7 100 3 92 19 2 0 0 0 7 14 2 2 0 0 2 4 0 0 0 6 0 0 0 0 0 0 + 23 - - c = - 3 ་ ་