### NR 421 – Assignment #8

### Advanced Cluster Sampling

**Objective: **This assignment will ask you to work with real-world data to implement one- and two-stage cluster sampling designs. You will also demonstrate your ability to interpret descriptions of different sampling protocols and use statistical terminology to explain what is happening.

**Student Learning Outcomes:** Upon completing this assignment you should be able to:

- Apply one- and two-stage cluster sampling calculations to summarize an inventory.
- Show a mastery of sample design concepts.
- Demonstrate your ability to communicate sampling concepts.

1. You are taking over management of a 20-year-old plantation and have been asked to estimate the average height of trees in the plantation. The plantation contains 400 row-segments, each with 20 original planting spaces (but not an equal number of surviving trees due to differential mortality rates). A simple random sample of 8 row-segments is selected from the 400 segments that compose the plantation. All trees in the selected sampling row-segment have their height measured. What type of cluster sampling has been performed? Estimate the total number of surviving trees in the plantation and its associated variance. Calculate the average height of trees in the plantation and its associated variance.

2. Your company expects a 90% tree survival rating and an average of 1.9 feet per year of height growth to age 20. Determine at a 90% confidence interval if the plantation is on track to meet these expectations. (This means you should calculate a 90% confidence intervals for both tree survival and height, then determine if the expected parameters are contained within the intervals.)

3. For the following scenario, describe the sampling design being implemented using the terminology we have discussed. You should consider how the samples were located, how they were grouped, and the area they represent. You will be evaluated both on proper use of terms and on your writing.

Your organization established a set of permanent sampling points throughout its 600 acre forest empire. The objective of establishing this monitoring protocol was the assessment of periodic growth to be used in forest wide planning. The established design divided the population into 4 acre blocks in a spatial grid, from which 15 evenly spaced out blocks were selected. In each selected block, four 0.10 acre plots are randomly selected.

4. For the scenario described in question 3, the 2005 and 2015 cu ft volume for each plot in the system is given in the accompanying Excel file. From the provided data, determine the forest wide growth per acre per year and its associated variance.

5. If the products in your forest are valued at $1.38 per cubic foot, determine a 95% confidence interval of the annual increase in value for the entire forest. Write a statement about your confidence.