Baseball data. Exercise 32 of Chapter 2 described the population of baseball players in data file baseball.dat.

a. Take a stratified random sample of 150 players from the file, using proportional allocation with the different teams as strata. Describe how you selected the sample.

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b Find the mean of the variable logsal, using your stratified sample, and give a 95% CI.

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c Estimate the proportion of players in the data set who are pitchers, and give a 95% CI.

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d How do your estimates compare with those of Exercise 32 from Chapter 2?

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e Examine the sample variances in each stratum. Do you think optimal allocation would be worthwhile for this problem?

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f Using the sample variances from (e) to estimate the population stratum variances, determine the optimal allocation for a sample in which the cost is the same in each stratum and the total sample size is 150. How much does the optimal allocation differ from the proportional allocation?