1) (Use R; submit your R code) The data file baseball.csv contains statistics on 797 baseball players from the rosters of all major league teams in November, 2004. a) Take a stratified sample of 150 players from the file, using proportional allocation with the different teams as strata. b) Find the mean of the variable logsal using your stratified sample, and interval. give a 95% confidence c) Estimate the proportion of players in the data set who are pitchers, and give a 95% confidence interval. d) Estimate the sample variances in each worthwhile for this problem? Here is the baseball.csv data. stratum. Do you think optimal allocation would be B с D E F G H J K L M N ° P Q R S T U V W X Y Z AA AB AC AD AE AF 1 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 3 4 ANA AL davanje0 375000 CF 108 5 ANA AL donnebro 375000 P 5 6 ANA AL eckstda0 2150000 SS 142 136 7 ANA AL erstada0 7750000 1B 125 124 8 ANA AL escobke0 5750000 P 1 9 ANA AL figgicho 320000 3B 148 10 ANA AL glaustro 9900000 3B 58 11 ANA AL greggke0 301500 P 5 12 ANA AL guerrvlo 1.1E+07 RF 156 143 13 ANA AL guilljoo 2200000 LF 148 14 ANA AL haltesh0 575000 3B 46 15 ANA AL kenneado 2500000 2B 144 16 ANA AL lackejoo 375000 P 2 17 ANA AL molinbe0 2025000 C 97 18 ANA AL molinjo0 335000 C 73 19 ANA AL ortizra0 3266667 P 1 20 ANA AL pauljo01 335000 C 46 21 ANA AL percitro 7833333 P 22 ANA AL rodrifro 375000 P ww 23 ANA AL salmoti0 9900000 RF 60 24 ANA AL seleaa01 8666667 P 1 25 ANA AL shielsco 375000 P 3 26 ANA AL washbja0 5450000 P 3 27 ANA AL weberbe0 900000 P 18 28 ARI NL alomaro0 1000000 2B 38 29 ARI NL baergca0 1000000 1B 79 30 ARI NL bautida0 4000000 RF 141 31 ARI NL choatra0 325750 P 69 32 ARI NL cintral0 335000 SS 154 33 ARI NL colbrgro 2750000 1B 20 34 ARI NL daiglca0 300000 P 11 35 ARI NL desseelo 4000000 P 36 36 ARI NL estalbo0 550000 C 7 8ཎྚཎ॰8ཊཿ་8°Nསྐྱལྐ⌘hl༠༠°nཟླ༠༢°ཀླ༥%°8༄༠༠ 92 2375 211 5 2 1 NA 112 442 57 133 34 625 8 30 3 4 NA 3 3 0 27 743 75 1 0 1 NA 108 285 41 0 126 2 3575 198 3196 986 66 33 625 16 80 2116 57 19 495 11 27 0 263 2 3702 308 135 3471 266 22 640 26 138 3675 255 32 595 15 89 2286 597 57 1573 441 14 384 6 16 504 134 0 149 1 0 252 5 5 117 15 24 396 3 0 316 6 25 448 3 0 67 0 23 610 48 4 107 32 135 3536 265 0 152 3 125 3297 141 1 27 7 10 147 5 9 256 5 3 92 19 288222522482512239-022034802-622 0 Ο ΝΑ 5 0 0 6 75 NA 142 566 92 156 4 83 NA 125 495 0 1 NA 1 2 79 0 146 11 9 NA 148 577 83 171 2 2 NA 58 207 47 0 1 NA 5 0 0 9 2 NA 156 612 124 206 6 1 NA 148 565 88 10 2 NA 46 114 10 12 71 NA 144 468 70 0 1 NA 2 2 0 3 5 6 97 337 36 37 3 4 3 73 203 26 2 1 NA 1 3 0 1 2 2 46 70 11 0 Ο ΝΑ 3 0 0 0 Ο ΝΑ 3 0 0 0 Ο ΝΑ 60 186 15 2 2 NA 1 1 0 1 Ο ΝΑ 3 1 0 1 2 NA 3 5 0 0 Ο ΝΑ 18 0 0 3 10 NA 38 110 14 0 2 NA 79 85 6 4 1 NA 141 539 64 0 1 NA 69 1 0 15 61 NA 154 564 56 ༢॰R°g¥°⪜g• 8 8ཀླg☁%%° °°!¥°༠ས༠༣8g°ཝ་ 20 1 14 75 2 1 29 75 6 1 0 3 3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 79 11 4 7 34 18 3 46 54 2 0 1 5 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 24 1 2 35 16 5 42 49 1 13 14 2 11 0 29 1 7 69 16 1 37 74 1 4 3 4 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 22 17 5 60 34 13 49 94 0 0 10 2 6 0 52 11 1 18 42 2 3 31 52 3 3 0 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 39 2 39 126 15 3 52 74 14 8 0 8 19 0 166 28 3 27 104 5 4 37 92 5 15 0 3 14 0 23 5 0 4 13 1 1 7 30 0 0 0 0 3 0 130 20 5 10 48 15 5 41 92 7 13 9 2 10 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 93 13 0 10 54 0 1 18 35 1 2 2 4 18 0 53 10 2 3 25 4 1 10 52 0 0 5 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 17 3 0 2 10 2 1 7 17 0 0 3 1 2 0 0 0 0 0 0 0 0 0 0 Ο ΝΑ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 47 7 0 2 23 1 0 14 41 0 2 0 4 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 2 0 0 0 1 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 34 5 2 3 16 0 2 12 18 0 1 2 0 2 0 20 2 0 2 11 0 0 6 12 0 3 0 0 7 0 154 27 1 11 65 6 2 35 66 2 4 1 3 20 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 148 31 7 4 49 3 3 31 59 2 2 12 4 11 0 0 Ο ΝΑ 20 27 1 3 0 0 0 1 0 0 1 5 0 0 0 0 0 0 0 Ο ΝΑ 11 17 2 2 2 0 0 0 0 0 0 7 0 0 1 0 1 1 1 Ο ΝΑ 36 18 0 3 2 0 0 0 0 0 3 3 0 0 4 0 1 1 0 0 0 7 14 2 2 0 0 2 4 0 0 0 6 0 0 0 0 0 0 = = 2000000 co ་ baseball (+