Question: 1. Baseball data. a Use the population in the file baseball.dat to take a one-stage cluster sample with the teams as the psus. Your sample

1. Baseball data. a Use the population in the file baseball.dat to take a one-stage cluster sample with the teams as the psus. Your sample should have approximately 150 players altogether. Describe how you selected your sample. b Draw side-by-side boxplots of logsal for the teams in your sample. c Use your sample to estimate the mean of the variable logsal, and give a 95% CI. d Estimate the proportion of players in the data set who are pitchers, and give a 95% CI. 2. Baseball data: Two-stage sample. a estimate the population value of R2 If we treat teams as the psus, and if all teams had the same size, what would the optimal subsampling size be (assume that c1 = c2). b Use the population in the file baseball.dat to take a two-stage cluster sample with the teams as the psus, using the subsampling fraction from part (a).Your sample should have approximately 150 players altogether. Describe how you selected your sample. c Draw side-by-side boxplots of logsal for the teams in your sample. d Use your sample to estimate the mean of the variable logsal, and give a 95% CI. e Estimate the proportion of players in the data set who are pitchers, and give a 95% CI. 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337500 P 500000 P 345000 RF 1800000 P 300000 CF 139 147 85 57 120 2 77 144 1 41 145 40 67 45 117 103 131 78 48 32 30 107 33 64 140 5 20 113 5 27 95 153 51 71 84 64 92 13 83 34 122 35 31 154 149 142 135 14 30 109 75 32 145 10 5 136 112 2 152 153 76 54 3 5 11 2 119 2 157 157 138 1 5 13 53 91 3 3 3 6 108 2 159 4 4 107 1 76 61 49 3 4 125 29 7 122 132 0 0 115 0 0 59 0 2 138 5 0 18 40 48 117 7 0 33 32 88 31 45 17 0 22 0 0 28 23 141 0 0 0 0 43 0 14 32 110 0 32 150 148 139 76 0 31 3 0 31 125 9 0 120 40 0 115 147 11 46 4 0 8 14 115 30 85 142 110 0 2 5 3 80 8 1 22 0 102 15 154 3 0 77 15 3 0 46 3 0 60 0 6 3244 88 246 12 20 3392 214 11 4 0 279 6 21 2 0 108 2 5 2 0 2971 242 315 16 74 4 0 0 0 0 158 2 7 1 0 1607 527 42 5 59 3 0 0 0 0 152 2 5 0 0 3657 341 3 2 2 136 8 1 0 0 196 5 6 0 1 393 9 10 0 0 1132 89 4 3 1 1320 67 158 5 29 3066 697 56 1 6 241 28 21 1 5 134 1 4 1 0 571 18 51 1 6 675 5 22 3 1 2379 801 55 4 69 582 13 25 2 2 1299 349 18 2 4 504 53 1 2 1 5 0 0 0 0 388 10 20 2 1 12 3 0 0 0 30 1 3 0 0 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