Use the data in file integerwt.dat for this exercise. The strata are constructed with
N1 =200, N2 =800, N3 =400, N4 =600.
a. Take a stratified random sample with n1 = 50, n2 =50, n3 =20, and n4 =25.
Calculate the sampling weight wi for each observation in your sample (the sample sizes were selected so that each weight is an integer).
b. Using the weights, estimate yU, S2, and the 25th, 50th, and 75th percentiles of the population.
c. Now create a “pseudo-population” by constructing a data set in which the data value yi is replicated wi times. Your pseudo-population should have N = 2000 observations. Estimate the same quantities in (b) using the pseudo-population and usual formulas for an SRS. How do the estimates compare with the estimates from (b)?