Description
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: 𝝈𝑨
𝟐
= 0 vs. Ha: 𝝈𝑨
𝟐 ≠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 𝝈𝑨
𝟐
.
c. How much of total variation in a single observation is attributed to differences between batches?