Four methods of manufacturing penicillin were compared in a randomized block design. The blocks are blends of the raw material, corn steep liquor, known to be quite variable. The yield of each method for 5 blends is given below:
| Method |
Blend |
Yield |
| A |
1 |
89 |
| A |
2 |
84 |
| A |
3 |
81 |
| A |
4 |
87 |
| A |
5 |
79 |
| B |
1 |
88 |
| B |
2 |
77 |
| B |
3 |
87 |
| B |
4 |
92 |
| B |
5 |
81 |
| C |
1 |
97 |
| C |
2 |
92 |
| C |
3 |
87 |
| C |
4 |
89 |
| C |
5 |
80 |
| D |
1 |
94 |
| D |
2 |
79 |
| D |
3 |
85 |
| D |
4 |
84 |
| D |
5 |
88 |
a) Estimate the method effects and the blend effects
b) Construct and ANOVA table. Is there significant difference between the methods? Are there significant differences between the blends?
c) Check the normality and constant variance assumptions by making residual plots.
d) If the blends were randomly selected, estimate the variance in yield due to blends.