STAT 420
Fall 2007
Homework #10
(10 points)
(due Friday, November 9, by 3:00 p.m.)
1.
An engineer is investigating the strength of concrete beams made from four types
of cement and employing three curing processes. The breaking strengths are
measured and are presented below.
Curing
Cement
Type
Process
A
B
C
D
1
14
6
22
10
2
15
8
20
7
3
10
7
18
7
a)
List an appropriate model and the underlying assumptions for this situation.
b)
Construct the ANOVA table and test for differences in cement types and curing
processes. Assume a 5-percent significance level.
a)
Y
i
j
=
μ
+
α
i
+
β
j
+
ε
i
j
,
i
= 1, 2, 3,
j
= 1, 2, 3, 4,
α
1
+
α
2
+
α
3
= 0,
β
1
+
β
2
+
β
3
+
β
4
= 0,
(
Curing Process
)
(
Cement Type
)
ε
i
j
are independent
N
(
0,
σ
2
) random variables.
b)
> Str <- c(14, 6,22,10,15, 8,20, 7,10, 7,18, 7)
> Cur <- c( 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3)
> Cem <- c( 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4)
>
> summary(aov(glm(Str ~ factor(Cur) + factor(Cem))))
Df Sum Sq Mean Sq F value Pr(>F)
factor(Cur) 2 14.00 7.00 2.625 0.1517037
factor(Cem) 3 318.00 106.00 39.750 0.0002361 ***
Residuals 6 16.00 2.67
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1