### NR 421 – Assignment #4

### Sample Allocation and Summarizing Stratified Stand Data

**Objective:** This assignment will ask you to explain the process and benefits of stratified data collection in natural resource management. This will require you to perform and contrast different sample allocation approaches and also summarize data collected from multiple strata.

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

- Describe the benefits and limitations of stratified sampling.
- Utilize sampling allocation strategies to set up a stratified sample.
- Develop a more advanced understanding of statistical equations.
- Apply the statistics for computing overall population parameters from a stratified sample.

1. What is stratified random sampling and what are three reasons we use it?

2. What are the steps in the stratification process?

3. What are the three types of allocation in stratified random sampling, provide their formulas and define their parameters?

4. You are given the following unit stratification information and told to allocate 160 – 1/10 acre plots. Calculate how many plots you would allocate to each strata using proportional allocation.

5. Now allocate the 160 plots using Neyman allocation.

6. Calculate the strata mean and variance of grazable biomass (tons) per acre from the stratified sampling of 1 m^{2} plots (lbs/m^{2}), each stratum is 40 acres in size. Assume sampling with replacement. Does this seem to be a good stratification of the population? Explain your answer. The data is available in the Excel sheet on the website. *Caution:* Convert stratum Standard Deviation to Variance instead of directly calculating Variance to avoid unit converstion issues.

7. Calculate the following combined statistics for the inventory in question #7, assuming sampling with replacement.

Combined mean tons per acre:

Combined variance:

8. Using your calculations from question #7 and what you know from question #6, compute the 90% confidence interval for how many months (assuming 30 days per month) the entire population can support a herd of 800 sheep if each animal requires 2.6 pounds of forage per day. As responsible managers we only want the herd to eat 60% of the forage. Write a statement about your confidence.

9. Using the computed cubic foot timber volume per plot provided from a cruise of 1/10 acre plots, calculate the sampling intensity for each stratum and the combined mean and variance per acre, assuming sampling without replacement. Does this seem to be a good stratification of the population? The data is available in the Excel sheet on the website.

10. If you decide to harvest only Strata B from question #9, at a 90% confidence level what would be the maximum profit you would expect if you can sell the material for $3.18 per cu ft.