10.2 Consider a simple random sample of size n sampled froma finite population of size N, with r respondents andm= n−r nonrespondents, and let yR and s2 R be the samplemean and variance of the respondents’ data, and yNR and s2 NR the sample mean and variance of the imputed data. Show that the mean y∗ and variance s2

∗ of all the data can be written as y∗ = (ryR + myNR)∕n and s2

∗ = ((r − 1)s2 R + (m − 1)s2 NR

+rm(yR − yNR)2∕n)∕(n − 1).