STUDENT NO: 42402115
SAMUKELISIWE MZILA
AGP4701
ASSIGNMENT NO 2 , SEMESTER 2 2024
,SEMESTER 2
ASSIGNMENT 2
QUESTION 1
To address the zoologist's study of the gains in weight of male rats
under the specified feeding treatments, we will follow the outlined
tasks step-by-step.
1.1 List out the six treatments and name the factorial experiment
The six treatments can be identified by combining the factors of
sources of protein and the amount of protein.
Treatments:
1. Beef, High protein
2. Cereal, High protein
3. Pork, High protein
4. Beef, Low protein
5. Cereal, Low protein
6. Pork, Low protein
Factorial Experiment:
This is a 2x3 Factorial Experiment:
- Factor A (Sources of Protein): 3 levels (Beef, Cereal, Pork)
- Factor B (Amount of Protein): 2 levels (High, Low)
1.2 Compute the ANOVA
Given the data, we need to compute the ANOVA to analyze the
variance among the treatments. The following components will be
calculated:
Step 1: Organize the Data
- Group data based on treatments.
, | Treatment | Data | Total | Mean |
|-------------------------|------------------------------------------|-------|--------|
| Beef, High protein | 73, 90, 102, 118, 104 | 487 | 97.4 |
| Cereal, High protein | 98, 107, 74, 96, 88, 111 | 574 | 95.7 |
| Pork, High protein | 94, 79, 80, 102, 78, 105 | 438 | 86.1 |
| Beef, Low protein | 90, 49, 76, 90, 82, 74, 100 | 461 | 65.9 |
| Cereal, Low protein | 107, 95, 81, 67, 58 | 408 | 81.6 |
| Pork, Low protein | 49, 82, 73, 98, 83 | 385 | 77.0 |
Step 2: Calculate the Overall Statistics
- G-Total = 5272, G-Mean = 87.87
- Number of treatments (k) = 6
- Total number of observations (N) = 36
Step 3: Sum of Squares
-SS Total (SST :
\[
SST = \sum (X_{ij}- \bar{X})^2
\]
- **SS Treatments (SSTreat)** :
\[
SSTreat = \sum \frac{n_i (\bar{X}_i - \bar{X})^2}
\]
- **SS Error (SSE)** :
\[
SSE = SST - SSTreat
\]
Calculation of Sum of Squares
1. Calculate the Overall Mean (\(\bar{X}\)): 87.87
2. Calculating SSTreat:
SSTreat = \frac{6}{6}((487-87.87)^2 + (574-87.87)^2+(438-
87.87)^2+(461-87.87)^2+(408-87.87)^2+(385-87.87)^2)
SAMUKELISIWE MZILA
AGP4701
ASSIGNMENT NO 2 , SEMESTER 2 2024
,SEMESTER 2
ASSIGNMENT 2
QUESTION 1
To address the zoologist's study of the gains in weight of male rats
under the specified feeding treatments, we will follow the outlined
tasks step-by-step.
1.1 List out the six treatments and name the factorial experiment
The six treatments can be identified by combining the factors of
sources of protein and the amount of protein.
Treatments:
1. Beef, High protein
2. Cereal, High protein
3. Pork, High protein
4. Beef, Low protein
5. Cereal, Low protein
6. Pork, Low protein
Factorial Experiment:
This is a 2x3 Factorial Experiment:
- Factor A (Sources of Protein): 3 levels (Beef, Cereal, Pork)
- Factor B (Amount of Protein): 2 levels (High, Low)
1.2 Compute the ANOVA
Given the data, we need to compute the ANOVA to analyze the
variance among the treatments. The following components will be
calculated:
Step 1: Organize the Data
- Group data based on treatments.
, | Treatment | Data | Total | Mean |
|-------------------------|------------------------------------------|-------|--------|
| Beef, High protein | 73, 90, 102, 118, 104 | 487 | 97.4 |
| Cereal, High protein | 98, 107, 74, 96, 88, 111 | 574 | 95.7 |
| Pork, High protein | 94, 79, 80, 102, 78, 105 | 438 | 86.1 |
| Beef, Low protein | 90, 49, 76, 90, 82, 74, 100 | 461 | 65.9 |
| Cereal, Low protein | 107, 95, 81, 67, 58 | 408 | 81.6 |
| Pork, Low protein | 49, 82, 73, 98, 83 | 385 | 77.0 |
Step 2: Calculate the Overall Statistics
- G-Total = 5272, G-Mean = 87.87
- Number of treatments (k) = 6
- Total number of observations (N) = 36
Step 3: Sum of Squares
-SS Total (SST :
\[
SST = \sum (X_{ij}- \bar{X})^2
\]
- **SS Treatments (SSTreat)** :
\[
SSTreat = \sum \frac{n_i (\bar{X}_i - \bar{X})^2}
\]
- **SS Error (SSE)** :
\[
SSE = SST - SSTreat
\]
Calculation of Sum of Squares
1. Calculate the Overall Mean (\(\bar{X}\)): 87.87
2. Calculating SSTreat:
SSTreat = \frac{6}{6}((487-87.87)^2 + (574-87.87)^2+(438-
87.87)^2+(461-87.87)^2+(408-87.87)^2+(385-87.87)^2)
