### NR 421 – Assignment #7

### Introduction to Cluster Sampling

**Objective: **This assignment will ask you to contrast the use of stratified sampling and cluster sampling in natural resource management. You will demonstrate you master of concepts related to sampling units as you begin performing cluster sampling calculations.

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

- Describe the differences between and when to use stratified vs cluster sampling.
- Apply one-stage cluster sampling calculations to summarize an inventory.
- Show a mastery of concepts surrounding the term sampling unit.

1. What are the two reasons we use cluster sampling?

2. How is cluster sampling different from stratified sampling? Explain the difference in the between and within variance of clusters vs strata.

3. You perform a cluster sample in which you visit 25 clusters that each have 4 elements in them, what is your ‘n’ value for the statistics?

4. How could you increase the variability within a cluster?

5. You are managing a nursery and want to estimate the average root to shoot ratio (DRC/Height) of individual Douglas-fir (*Pseudotsuga menziesii*) seedlings and its associated variance. The greenhouse you have the Douglas-fir in has been divided into 400 growing blocks, each containing 4 seedlings. A simple random sample of 16 growing blocks is selected from the 400. Within each block you measure the 4 seedlings for their diameter at root collar (DRC) and height. (One-stage cluster sampling)

6. The desired root to shoot ratio for Douglas-fir is 0.795 at an 95% confidence level, determine if your crop of seedlings is significantly different from this value. Make this determination by calculating a 95% confidence interval about the mean seedling root to shoot ratio for your Douglas-fir in question 5, then write a state about if your seedlings depart from this desired ratio.