### F 321 – Assignment #3

### Probability Sampling and Forest Structure Calculations

**Objective:** This assignment will ask you to explore concepts related to probability sampling and how this related to forest inventory. Additionally, you will begin to master the quantitative skills needed for summarizing forest structural parameters and inferential statistics.

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

- Describe the concepts of precision and accuracy within probability sampling.
- Explain the difference between sampling with replacement and without replacement.
- Calculate basic forest structure parameters.
- Express your confidence in a population parameter.

1. Define the following terms:

- Precision
- Accuracy

2. Does a sample provide you an estimate of accuracy or precision? Explain yourself.

3. What is the difference between a sample and a census, what are the benefits of both?

4. What does the Central Limit Theorem state and why is it important to sampling?

5. What is a simple random sample and what does it mean about the relationship between samples?

6. What are the two types of simple random sampling, describe the difference between them and what it means for the probability of selection?

7. What are the three requirements of a sampling design?

8. What assumption is necessary to use the statistics for sampling with replacement?

9. What would “n” and “N” be when inventorying a stand of 80 acres with 20 1/10 acre plots, using sampling without replacement?

10. Complete the calculation for volume per acre in plot #6, assuming trees are perfect cylinders and that plots are 1/20^{th} acre in area.

11. Provide the following statistics for plot #6 of the Preliminary Stand Exam Data in question #10:

- Quadratic Mean Diameter

- Trees per acre

- Basal Area per Acre

12. Calculate the mean volume, variance, coefficient of variation, and standard error per acre for the 6 plots in question #10.

13. Using what you calculated in question #12, determine how many 1/20^{th} acre plots you would need to estimate the mean volume per acre in the stand to within 8% at a 95% confidence level. Assume the stand is 42 acres and determine if we are concerned with the finite population correction factor.

14. Using what you calculated in #12, determine how many 1/20^{th} acre plots you would need in order to estimate the mean volume per acre within the stand to within 275 cu ft at a 95% confidence level. The stand is 57 acres, determine if we are concerned with the finite population correction factor.

15. What would be our new estimates of variance, standard deviation, and coefficient of variation if we decide to change our sampling design in question #10 from 1/20 acre plots to 1/10 acre plots?

16. You have a 120 acre stand that you inventory with 20 1/10 acre plots, from the plots you calculate a mean Vol/Acre of 500 cu ft and a standard deviation of 92 cu ft/Acre. If you sell the stand for $3.65 per cu ft, with 90% certainty what would be the maximum value you could receive?

17. You inherit a clinometer which only has numbers on it. Describe how you would determine which scales the clinometer has, presuming you do not have another to compare with.

**Extra Credit:** After reading Statistics for Practical People answer the following: (10 points)

- Give an example of the two biggest biases the author says we should be concerned with.
- What does the author suggest is the reason we should care about sampling design?