FR 3218/5218 Spring 2008

Due February 4, 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 hw2DAT_08.xls.

1. A small sawmill hired a new sawyer and conducted a mill study to determine the sawyer's efficiency. A random sample of 28 of the first 500 logs sawn by the sawyer were carefully scaled using the International 1/4-inch scale (the mill's standard). The logs were cut and mill scale also found. Percent under- or over-run was computed for each log (data are in worksheet Mill Study). See section 6-8 of your text for information about under/over-run computation.

1. Estimate mean under/over-run. Compute a standard error for the estimate.
2. Construct a 90% confidence interval for mean under/over-run.
3. If the International 1/4-inch scale of all the logs processed by the sawyer was 50 MBF, how many MBF would have been wasted by the sawyer's ineptitude? Provide a standard error for your estimate. (MBF is thousand board feet)
4. Using the data from the current sample, determine the number of logs needed to estimate under/over-run with a standard error of 10%.
5. Assign the value 1 to each log in the sample with an under-run; assign the value 0 to logs with an over-run. Use these coded data to estimate the proportion of logs where there was under-run. Compute a standard error for the estimate.

2. Interest lies in estimating the amount of residue left on harvested sites that could be utilized for energy. The study area is a “working circle” about an existing biomass fuel plant. In 2007 there were 59 harvested sites identified in the working circle; site acreage was determined from aerial photography. Unequal probability sampling, with probability proportional to site acreage, was used to select 12 sites for ground survey. The ground survey produced an estimate of usable residue (in tons) on the site. Refer to the Biomass Energy worksheet.

1. Which sites are in the sample?
2. Estimate tons of residue available in the plant’s working circle for 2007. Obtain a standard error of the estimate as well.
3. What are you assuming about the relationship between tons of usable residue and site acreage for the unequal probability sample to be more efficient than a simple random sample of sites for estimating tons of residue available in the plant’s working circle for 2007? What other factors (characteristics of the harvest sites) might deter from the effectiveness of unequal probability sampling?