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

10.2. Consider a simple random sample of size n with r respondents and m ¼ n r nonrespondents, and let yR and s2 R be the sample mean and variance of the respondents’ data, and yNR 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 ðryR þ myNRÞ n and s 2 * ¼ ½ðr 1Þs2 R þ ðm 1Þs2 NR þ rmðyR yNRÞ 2 =n ðn 1Þ :