(Requires computing.) Use the population in agpop.dat for this exercise.
a Take 500 SRSs, each of size n = 40, from the data set. For each SRS, calculate the sample mean y¯, the poststratified mean y¯post from (4.21), the estimated variance of y¯, and the estimated variance of y¯post using (4.22).
b Calculate the sample variance of the 500 values of y¯. This gives an estimate of the true value of V(y¯). Compare your value with the average of the 500 values of Vˆ (y¯). Since Vˆ (y¯) is an unbiased estimator of V(y¯) for any sample size, these values should be close.
c Calculate the sample variance of the 500 values of y¯post. This gives an estimate of the true value of V(y¯post). Compare your value with the average of the 500 values of Vˆ (y¯post).
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