FR 3218/5218 Spring 2007

Due January 29, 2007

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 Grader 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). You may also use a statistical package if you wish. If you do, turn in printouts that are annotated so that the Grader can follow the calculations. All data for this assignment are in the Excel workbook hw2Data_07.xls.

1. A forest manager has been asked by his supervisor to estimate the number of permanent deer stands on 6,600 acres of the company's land. The manager decides to randomly sample blocks within the forest. Blocks are 40 acres in size, so there are 165 such blocks. Sampling is done without replacement. A team of student interns is sent out to locate all permanent deer stands in the sampled blocks. The students have time to survey 25 blocks. Data are in the worksheet Deer Stands.

1. Estimate mean number of permanent deer stands per 40 acre block. Compute a standard error for the estimate.
2. Estimate the total number of permanent deer stands on the entire forest. Compute a standard error for this estimate.
3. Construct a 95% confidence interval for the total number of permanent deer stands on the entire forest.
4. Using the data from your current sample, determine the number of 40 acre blocks needed to estimate the total number of permanent deer stands on the entire forest with a desired standard error of 10%.
5. Assign the value 0 to each block in your sample that has 0 or 1 permanent deer stands; assign the value 1 to blocks that have 2 or more permanent deer stands. Use these coded data to estimate the proportion of blocks with 2 or more permanent deer stands (possibly an unacceptable number). Compute a standard error for the estimate.

2. An organization representing forestry professionals is in the process of undertaking a review of continuing education programs for its members. The organization has asked you to estimate the total number of continuing education credits organization members have taken within the past year. You meet with the membership chair and obtain from her a file that lists the membership numbers for each of the 65 chapters in the organization. You decide that an unequal probability sample would work here. You randomly generate 12 numbers between 1 and 3478, the total number of members in the organization, and use them to select 12 chapters with probability proportional to membership size. For each chapter sampled you ask the chapter president to determine the total number of continuing education credits their members took in the past year. Refer to the Continuing Education worksheet.

1. Which chapters were in the sample?
2. Estimate the total number of continuing education credits members took last year. Obtain a standard error of the estimate as well.
3. What are you assuming about the relationship between size of chapters and number of continuing education credits for the unequal probability sample to be more efficient than a simple random sample of chapters for estimating total number of continuing education credits members took last year?