In Example 6.11, we calculated the with-replacement variance for HT. In this example, the sampling fraction n/N is 1/3, so the with-replacement variance is likely

In Example 6.11, we calculated the with-replacement variance for ṫHT. In this example, the sampling fraction n/N is 1/3, so the with-replacement variance is likely to overestimate the without-replacement variance. The joint inclusion probabilities for the psus are given in file classppsjp.dat, and can also be obtained by running the SAS program given on the website.
a. Calculate ṼHT (ṫHT) and ˆVSYG (ṫHT) for this data set.
b. SAS software approximates the without-replacement variance in unequal-probability sampling using

Calculate this approximation for the class data.

, n