Chapter 11: Section 11.1, Exercise 10. “The strength of concrete used in commercial …”
Here is the ANOVA table for this data set:
Analysis of Variance for Strength
Source
DF
SS
MS
F
P
Batch
9
86.793
9.644
7.22
0.000
Method
2
23.229
11.614
8.69
0.002
Error
18
24.045
1.336
Total
29
134.067
Follow these instructions:
a. With =0.05, perform the 2 tests of hypothesis:
◦ (Factor A = Batch) H0: = 0 vs. Ha: ≠0
◦ (Factor B = Method) H0: β1= β2= β3 vs. Ha: H0 is false. Follow the 4-step procedure and use the P-values above.
b. Suppose that Factor A (Batch) is a random effect. Compute by hand an estimate of .
c. How much of total variation in a single observation is attributed to differences between batches?
