FR 3218/5218 Spring 2008

Due February 13, 2008

It is important that you show your work. Credit cannot be given if answers are not accompanied by intermediate calculations that demonstrate how you arrived at the final solution. The TA will look to the intermediate calculations to determine the level of partial credit to be granted for wrong answers. If you turn in a printout of a spreadsheet be sure to include the formulas you used to calculate all intermediate and final estimates (see Excel insert in the solution set for Assignment 1); better yet, e-mail the spreadsheet file to the TA. You may also use a statistical package if you wish. If you do use a statistical package, turn in printouts that are annotated so that the TA can follow the calculations. All data for this assignment are in the Excel workbook hw3DAT_08.xls.

1. A city forester needs to estimate the cost of removing exotics from lands administered by the city. The city is divided into 1250 equal-sized management units. The forester decides to use stratified random sampling of management units with strata: parks (50 units total), wildlands (175 units total), residential (625 units total), and business (400 units total). For each management unit selected (sampled), the forester obtains an estimate of cost of removal for the management unit. Data are in the Exotic Removal worksheet.

1. Estimate the cost of removal per management unit for each stratum and obtain associated standard errors.
   
2. Estimate the total cost of removal for the city and provide a 90% confidence interval for total cost. (of course you'll first need to estimate the mean cost per management unit across all strata, and obtain a standard error of that estimate)
   
3. Was stratified sampling sensible in the example? Why or why not? (consider our discussion of under what conditions stratified sampling excels)
   

2. Referring back to the previous question (using those data to estimate variances):

1. Compute the total number of management units that would need to be observed, as well as the number of management units by stratum, under proportional allocation to achieve a desired standard error of ten dollars per management unit.
   
2. Compute the total number of management units that would need to be observed, as well as the number of management units by stratum, under optimal allocation (assuming equal observation costs in each stratum) to achieve a desired standard error of ten dollars per management unit.
   
3. Briefly discuss why the two allocations lead to sampling different total number of management units and management units by stratum allocations.
   

3. Your company is interested in purchasing the pine timberlands that another company has put up for sale. The seller conducted an inventory approximately 15 years ago and has provided you estimates of volume per acre by stand from the old inventory. For stands that have not been cut in the interim (300 such stands), you decide to select a random sample of 25 stands and cruise them to obtain current volume per acre. Using the old inventory you determine mean volume for the 300 stands of interest was 28 cords per acre (15 years ago). Other relevant data are in the Timber Purchase worksheet.

1. Compute the ratio-of-means estimate of current volume per acre for the 300 stands of interest and provide the standard error of the estimate.
   
2. Compute the regression estimate of current volume per acre for the 300 stands of interest and provide the standard error of the estimate.
   
3. Which estimator is most appropriate (if either)? Explain what you base your answer on?