One of the research focuses of the Research Farm at Ataturk University, Erzurum, Turkey, is on increasing meat quality and production in sheep. As part of this research, the sheep are sampled periodically in order to monitor their biological growth and provide estimates for the population means of specific traits of interest. Young sheep are very active animals and it is labor intensive to hold them secure during the measurement process. As a result, it is important to minimize the number of sheep included in these samples while still obtaining reliable information about the broader population. RSS can be used effectively to reduce the number of lambs that must be measured at each of these periodic samplings by taking advantage of readily available archival information about the birth weight of a lamb and its mother's weight at the time of mating, both of which are positively correlated with the lamb's weight throughout its growth cycle. Table 15.5 contains the birth weight, mother's weight at the time of mating, and the weight at 7 months for 224 lambs at the Research Farm of Ataturk University. Use the mother's weight at the time of mating as the auxiliary ranking variable and set size k = 3 to select an RSS (using SRSs without replacement throughout the ranking process) of size n = 21. Obtain the RSS estimate of the average 7-month weight for the entire population of 224 lambs based on the 7-month weights of these 21 lambs.
