Question

1. chapter 6: #6.28
2. chapter 8: #8.35
3. problem#3:

based on satellite images, a forest area in the amazon basin is divided into 14 types. foresters studied the four most commercially valuable types: alluvial climax forests of quality levels 1, 2, and 3, and mature secondary forest. they divided the area of each type into large parcels, chose parcels of each type at random, and counted tree species in a 20 - by 25 - meter rectangle randomly placed within each parcel selected. here are some details: (modified from textbook 8.41)

forest type	total parcels	sample size
climax 2	72	7
climax 3	31	3
secondary	42	4

a) what is sampling scheme of this study? and why we use it?
b) choose the stratified sample for secondary forest type. be sure to explain how you assigned labels to parcels. if you use table b, start at line 112.
line 112: 59636 88804 04634 71197 19352 73089 84898 45785
c) if the study does not care about the commercial viability of the forest, what would be the sample scheme that the researcher may have possibly adopted?

Explanation:

a) The sampling scheme is stratified sampling. It's used because the forest area is divided into different strata (forest types) based on commercial value, and samples are taken from each stratum. This ensures representation of each distinct forest - type and can lead to more precise estimates.
b) For the secondary forest type with 42 total parcels, label the parcels from 01 - 42. Using Table B starting at line 112, read two - digit numbers. Ignore numbers outside 01 - 42, duplicates, and continue until 4 unique numbers within 01 - 42 are obtained. These numbers correspond to the selected parcels.
c) If commercial viability is not a concern, a simple random sampling scheme could be adopted. In simple random sampling, all parcels in the entire forest area would have an equal chance of being selected without dividing the area into strata based on commercial value.

Answer:

a) Sampling scheme: Stratified sampling. Reason: To represent different forest - types and get more precise estimates.
b) Label parcels 01 - 42. Use Table B line 112, pick 4 unique two - digit numbers within 01 - 42.
c) Simple random sampling.