Consider the procedures used by the class to collect the proportional data (not
ID: 3047237 • Letter: C
Question
Consider the procedures used by the class to collect the proportional data (not the holly leaf data). Assume these data represent a sample of all evergreens of the campus. You may want to review Labs 3 and 4 before answering the questions below. The proportional data was collected by walking and as you walked you counted 20 trees and put them into one of the four categories below.
Table 2: proportional data
Tree type
Count
(out of 20)
Proportion ()
(out of 20)
American holly
8
.40
Southern magnolia
3
.15
Pine (any type)
3
.15
Other
6
.30
q) Is random sampling used in the procedures for collecting the proportional data? Explain.
r) Welcome to the real world: you do not have the resources to increase your sample size.
If you do not have the resources to increase your sample size, how could you change the procedures we used to improve our estimate of p? Describe an improved procedure in detail. (A suggested length is one-two paragraphs, meaning as much as half a page.)
Table 2: proportional data
Tree type
Count
(out of 20)
Proportion ()
(out of 20)
American holly
8
.40
Southern magnolia
3
.15
Pine (any type)
3
.15
Other
6
.30
Explanation / Answer
Given data table is as follows:
American Holly VS Southern magnolia
0.641059
American Holly VS Other
0.274641
Both Z values are less than 1.96 and hence at 5% LOS we conclude that two population proportions are same. It further means data is generated by adopting random sampling method.
In this method treat count (out of 20) for each category as a population and draw as many samples of appropriate size from these populations. We may get so many samples.
Following table will give possible samples of various sizes.
Sample size
American Holly (8)
Southern magnolia (3)
Pine (3)
Other (6)
1
8
3
3
6
2
28
3
3
15
3
56
1
1
20
4
70
-
-
15
5
56
-
-
6
6
28
-
-
1
7
8
-
-
-
8
1
-
-
-
Total
255
7
7
63
Category wise for each sample compute estimate of p and then for all sample obtain pooled estimate pf p. This estimate will provide better estimate of p
American Holly VS Southern magnolia
0.641059
American Holly VS Other
0.274641
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