draw a stratified sample using proportional sizes based on the Department variable

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boston <- read.csv( "http://people.bu.edu/kalathur/datasets/bostonCityEarnings.csv", colClasses = c("character", "character", "character", "integer", "character")) Create a subset of the dataset from Part1 with only the top 5 departments based on the number of employees working in that department. The top 5 departments should be computed using R code. Then, use %in% operator to create the required subset. (USE subset and %in% function) Use a sample size of 50 for each of the following. Set the start seed for random numbers as the last 4 digits of your BU id. a) Show the sample drawn using simple random sampling without replacement. Show the frequencies for the selected departments. Show the percentages of these with respect to sample size. b) Show the sample drawn using systematic sampling. Show the frequencies for the selected departments. Show the percentages of these with respect to sample size. c) Calculate the inclusion probabilities using the Earnings variable. Using these values, show the sample drawn using systematic sampling with unequal probabilities. Show the frequencies for the selected departments. Show the percentages of these with respect to sample size. d) Order the data using the Department variable. Draw a stratified sample using proportional sizes based on the Department variable. Show the frequencies for the selected departments. Show the percentages of these with respect to sample size. e) Compare the means of Earnings variable for these four samples against the mean for the data.

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