Problem 3. A forester wants to estimate the total number of farm acres planted in trees for a state. Since the number of acres of trees varies considerably with the size of the farm, he decides to stratify on farm sizes. The 240 farms in the state are stratified in one of four categories according to size. A stratified sample of 40 farms, selected by using proportional allocation, yields the results shown in the table below. Stratum N n yi Si 0 to 200 acres 84 14 64 33 200 to 400 acres 72 12 183 95 400 to 600 acres 54 9 341 130 600 acres or more 30 5 472 269 a) Provide an estimate of the total area (in acres) of trees on farms in the province, and give a margin of error on the estimate. b) Suppose one wishes to obtain a margin of error on the estimate of 5000 acres. Considering what precedes as a preliminary investigation, find the size of the sample needed to reach this bound if the Neyman distribution is used