2. A corporation wishes to obtain information on the effectiveness of a busi- ness machine. A number of division heads will be interviewed by telephone and asked to rate the equipment on a numerical scale. The divisions are located in North America, Europe and Asia. Hence, stratified sampling is used. The costs are larger for interviewing division heads outside North America. The accompanying table gives the costs per interview, approx- imate variances of the ratings, and N that have been established. The corporation wants to estimate the average rating with V(st) = 0.1. North America C₁ = $9 Europe C2 = $25 Asia C3 = $36 σ = 2.25 တို - σ = 3.24 0 σ = 3.24 N₁ = 112 N2 = 68 N3 = 39 (a) You recommended the use of optimal allocation (the best allocation scheme). Find the sample size n and the total sampling cost. (b) Your colleague argues that Neyman allocation is better because the total sample size n is smaller. Show him that your method is better because the total cost of Neyman allocation is larger.