# solution

(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 yÂ¯, the poststratified mean yÂ¯post from (4.21), the estimated variance of yÂ¯, and the estimated variance of yÂ¯post using (4.22).

b Calculate the sample variance of the 500 values of yÂ¯. This gives an estimate of the true value of V(yÂ¯). Compare your value with the average of the 500 values of VË† (yÂ¯). Since VË† (yÂ¯) is an unbiased estimator of V(yÂ¯) for any sample size, these values should be close.

c Calculate the sample variance of the 500 values of yÂ¯post. This gives an estimate of the true value of V(yÂ¯post). Compare your value with the average of the 500 values of VË† (yÂ¯post).

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