analysis of variance assignment (ANOVA)
Emilytutors
HW6.doc1. (20) A research specialist for a large seafood company investigated bacterial growth on oysters and mussels subjected to three different storage temperatures. Nine cold storage units were used. Three storage units were randomly selected to be used for each of the storage temperatures. Oysters and mussels were stored for two weeks in each of the cold storage units. The number of bacteria in each sample was observed. For the “seafood” variable, 1 means oysters and 2 means mussels.
|
storage unit |
temperature |
seafood |
Count |
|
1 |
0 |
1 |
40 |
|
1 |
0 |
2 |
1 |
|
2 |
0 |
1 |
6 |
|
2 |
0 |
2 |
6 |
|
3 |
0 |
1 |
187 |
|
3 |
0 |
2 |
97 |
|
4 |
5 |
1 |
1333 |
|
4 |
5 |
2 |
151 |
|
5 |
5 |
1 |
11186 |
|
5 |
5 |
2 |
2841 |
|
6 |
5 |
1 |
1668 |
|
6 |
5 |
2 |
594 |
|
7 |
10 |
1 |
17751 |
|
7 |
10 |
2 |
25215 |
|
8 |
10 |
1 |
646 |
|
8 |
10 |
2 |
156 |
|
9 |
10 |
1 |
12635 |
|
9 |
10 |
2 |
61877 |
a. (5) The investigator could have had three replications for the study by simply taking three random samples of each type of seafood from a single cold storage unit set at one temperature. In this way, only three cold storage units would have been needed for the study, one for each temperature. Explain the potential difficulty with the study, if it had been conducted this way.
b. (10) Suggest a model for this experiment
c. (5) Confirm whether your model is adequate. If not, fix the problem.
2. (25) The quality control department of a fabric finishing plant is studying the effect of several factors on the dyeing of cotton-synthetic cloth used to manufacture men’s shirts. Three cycle times, and two temperatures were selected, and three small specimens of cloth were dyed under each set of conditions by a set of three randomly selected operators. The finished cloth was compared to a standard, and a numerical score was assigned. The results follow.
|
|
Temperature |
||||||
|
|
|
300° |
|
|
|
350° |
|
|
|
|
Operator |
|
|
|
Operator |
|
|
Cycle Time |
1 |
2 |
3 |
|
1 |
2 |
3 |
|
|
23 |
27 |
31 |
|
24 |
38 |
34 |
|
40 |
24 |
28 |
32 |
|
23 |
36 |
36 |
|
|
25 |
26 |
29 |
|
28 |
35 |
39 |
|
|
|
|
|
|
|
|
|
|
|
36 |
34 |
33 |
|
37 |
34 |
34 |
|
50 |
35 |
38 |
34 |
|
39 |
38 |
36 |
|
|
36 |
39 |
35 |
|
35 |
36 |
31 |
|
|
|
|
|
|
|
|
|
|
|
28 |
35 |
26 |
|
26 |
36 |
28 |
|
60 |
24 |
35 |
27 |
|
29 |
37 |
26 |
|
|
27 |
34 |
25 |
|
25 |
34 |
24 |
a. (8) Fit a model suitable for this experiment
b. (5) Check if your model is adequate
c. (7) See if you can simplify the model from point (a)
d. (5) Calculate the percent of variability associated with each random source of variability. Which is the largest source of variability?
3. (25) An experiment was conducted in a completely randomized design to study the effect of insecticides and fertilizer, on the control of hornworm infestations on a crop plant. The insecticide types were four sources of bacillus, and two types of chemicals. There are 4 types of fertilizer. The number of worms present was counted before and after treatment. The results of the experiment are as follows.
|
|
Fertilizer |
|||||||
|
|
1 |
2 |
3 |
4 |
||||
|
Insecticide |
Before |
After |
Before |
After |
Before |
After |
Before |
After |
|
Bacillus 1 |
15 |
17 |
25 |
26 |
18 |
21 |
23 |
26 |
|
Bacillus 2 |
19 |
18 |
21 |
22 |
20 |
19 |
19 |
20 |
|
Bacillus 3 |
19 |
19 |
19 |
21 |
21 |
23 |
25 |
22 |
|
Bacillus 4 |
22 |
14 |
31 |
26 |
17 |
17 |
19 |
19 |
|
Chemical 1 |
17 |
5 |
22 |
6 |
26 |
13 |
18 |
10 |
|
Chemical 2 |
22 |
25 |
14 |
19 |
22 |
26 |
23 |
27 |
a. (10) Analyze the data using =0.1 and suggest a model for this experiment
b. (5) Check if the model you chose is adequate
c. (10) Assess which differences among insecticides and fertilizers are significant. Which of these products are the best? Are your conclusions statistically significant?
