5.9. Consider a simple random sample of size n with r respondents and m n ...

5.9. Consider a simple random sample of size n with r respondents and m ¼ n  r nonrespondents, and let y
R and s2 R be the sample mean and variance of the respondents’ data, and y
NR and s2 NR the sample mean and variance of the imputed data. Show that the mean and variance y
 and s2  of all the data can be written as y
 ¼ ðry
R þ my
NRÞ=n and s 2  ¼ ½ðr  1Þs 2 R þ ðm  1Þs 2 NR þ rmðy
R  y
NRÞ 2 =n=ðn  1Þ: