The following data are derived from a stratified sample of tire dealers taken in March 1945 (Deming and Simmons, 1946). The dealers were assigned to strata according to the number of new tires held at a previous census. The sample means yh are the mean numbers of new tires per dealer. (a) Estimate the gain in precision due to the stratification. (b) Compare this result with the gain that would have been attained from proportional allocation. Stratum Boundaries 1-9 10-19 20-29 30-39 Totals Nh Wh Th Sh 19,850 3,250 0.1315 13.0 1,007 0.0407 25.0 174.2 606 0.0245 38.2 320.4 24,718 0.9999 nh 0.8032 4.1 34.8 3000 92.2 600 340 230 4170