"Muck" is the rich, highly organic type of soil that serves as the primary growth medium for vegetation in the Florida Everglades. Because of the high concentration of organic material, muck can be destroyed over time by a variety of natural and human-made causes. Members of the Florida Game and Fresh Water Fish Commission staked out several plots in the Everglades. The depth of muck at each location was measured when each plot was marked and again 6 years later. The following table identifies a portion of the data (given in inches) obtained.
|
Plot
|
Initial Reading
|
Later Reading
|
Pot
|
Initial Reading
|
Later Reading
|
|
1
|
34.5
|
31.5
|
9 |
44.0
|
35.2
|
|
2
|
44.0
|
37.9
|
10 |
40.3
|
37.2
|
|
3
|
37.5
|
35.5
|
11 |
27.0
|
24.7
|
|
4
|
27.0
|
23.0
|
12 |
29.5
|
25.8
|
|
5
|
37.0
|
34.5
|
13 |
31.5
|
29.0
|
|
6
|
40.0
|
31.1
|
14 |
35.0
|
36.8
|
|
7
|
47.2
|
46.0
|
15 |
44.0
|
36.3
|
|
8
|
35.2
|
31.0
|
|
|
|
a. Test to see if there is sufficient evidence to indicate a decrease in average muck depth during the study period. Give bounds on the associated p-value. What would you conclude if you desired to implement anα = .01 level test? (Although you are free to take the necessary differences in any order that you prefer, the answer provided at the back of the book assumes that the differences were formed by taking later readings minus initial readings.)
b. Give a 95% confidence interval for the difference in mean muck depths at the end and beginning of the study. Interpret this interval. [See the remark following part (a).]
c. Give a 95% confidence interval for the initial mean muck depth in the portion of the Everglades in which the study was conducted.
d. Repeat the instructions of part (c) for later readings.
e. What assumptions are necessary to apply the techniques you used in answering parts (a) and (b)? Parts (c) and (d)?