Consider the first four (Arm Circumference (Arm Cir), BMI) pairs in the NHANES III data given in Table 15.2, namely,
(a) In part (a) of Problem 20 you listed the possible SRSs of size n = 2 that could be selected from this subset of four BMI values. Calculate the sample mean for each of these potential SRSs. Calculate the average of these SRS means and compare it with the mean of the full subset of four BMI values.
(b) In part (b) of Problem 20 you listed the possible ranked set samples of size n = 2 that could be selected from this subset of four BMI values using a set size of k = 2 and arm circumference as the auxiliary variable for the ranking process. Calculate the sample mean for each of these potential RSSs. Calculate the average of these RSS means and compare it with the mean of the full subset of four BMI values.
(c) What important properties of the SRS mean and the RSS mean are illustrated by what you found in parts (a) and (b)?
