Download NRM 340 – Problem Set #3

NRM 340 – Sampling Problem Set
You have been asked to sample a forest tract using 0.25 hectare plots to
estimate the mean tree height (meters). The tract contains three
distinct vegetation types. You want to show how stratification can
improve your estimate. (Obviously in a real sampling situation the raw
population data would be unknown, but here these data are given so that
you can set up new samples and compare sample estimates to true values).
Note the following:
a. The total population (N) = 60 and the total number of samples
(n) = 18 in all 3 designs. Blank cells indicate sampling units not
chosen.
b. The three strata are represented by different colors (red,
blue, and green).
7.6
8.5
7.7
6.1
7.0
9.1
6.7
8.4
11.3
27.8
17.8
25.7
Raw Population Data
9.1
7.8
3.6
7.0
9.3
3.3
10.7
6.5
3.6
9.1
6.5
4.5
6.3
5.3
3.4
6.7
7.4
4.7
7.7
9.3
3.7
5.5
8.5
5.6
23.6
14.3
29.4
27.7
15.7
21.4
29.8
16.6
21.1
24.6
26.7
21.2
Simple Random Sampling
7.6
9.1
3.6
3.3
10.7
6.5
6.1
9.1
6.3
9.1
6.7
8.5
Systematic Sampling
2.4
3.5
4.5
2.4
3.4
4.8
3.3
4.8
21.5
28.5
19.3
14.5
2.4
3.5
8.5
9.3
3.5
6.1
6.5
2.4
9.1
7.4
4.8
8.4
8.5
4.8
27.8
15.7
28.5
25.7
26.7
14.5
Stratified Random Sampling
3.6
7.0
7.0
9.1
6.7
3.4
7.4
5.5
27.7
27.8
16.6
26.7
19.3
25.7
4.7
3.7
8.5
14.3
4.8
21.4
29.8
24.6
1. Compute the sample mean, standard deviation, and standard error for
each of the above sampling designs.
2. Compare the differences between the sample estimates of the mean
for each of the above sampling designs and the true population mean.
Which estimate was most accurate? Why?
3. Determine the appropriate sampling intensity (n) for a simple random
sample within + 5% of the mean and a 95% confidence interval. Use
your estimates of the mean and standard deviation from question #1
as your pilot study estimate.
4. Use optimum allocation to distribute sample plots in the stratified
random sample design (maintaining n=18). Assume your estimates from
question #1 are your pilot study estimates.
5. (not related to the above questions) You have sampled a plantation of
2-year old white spruce seedlings to determine the survival rate. The
survey found 77 seedlings to be alive and 42 to be dead. Estimate the
proportion of live seedlings, the standard error and a 95% confidence
interval. The number of seedlings originally planted was 2400 (N =
2400),
Please present your work in a readable format, and show your work (i.e. show
what formulas you used, and any intermediate answers on the way to your
final answer for each question.)
This assignment is due at 10:30 a.m. on Friday November 20th.