Stat 512 – 2
Solutions to Homework #12
Dr. Simonsen
Due Friday, December 2, 2005 by 4:30pm
1.
KNNL 25.3:
In each of the following cases, indicate whether ANOVA model I or model II is
more appropriate and state your reasons:
(a)
In a study of absenteeism at a plant, the treatments are the three 8-hour shifts.
There are only three shifts, and differences among these are of interest.
Therefore a fixed effects
model (I) is appropriate.
(b)
In a study of employee productivity, the treatments are 10 production employees
selected at random from all production employees in a large company.
These employees are selected at random to represent all employees.
Therefore a random effects
model (II) is appropriate.
(c)
In a study of anticipated annual income at retirement, the treatments are the four types
of retirement plans available to employees.
There are only four plans, and differences among these are of interest.
Therefore a fixed effects
model (I) is appropriate.
(d)
In a study of tire wear in 18-wheel trucks, the treatments are four tire locations
selected at random.
The four locations were selected at random to be representative of the entire tire, and are not of
interest in themselves.
Therefore a random effects model (II) is appropriate
2.
KNNL 25.13:
In a two-factor ANOVA study with a = 3, b = 2, and n = 5, the two factor
effects are both random with
σ
2
= 5.0,
Assume that
ANOVA model (24.39)) is applicable.
2
2
2
8.0,
10.0, and
6.0.
α
β
αβ
σ
=
σ
=
σ
=
(a)
Obtain E{MSA}, E{MSB}, and E{MSAB}
(
)
(
)
(
)
2
2
2
2
2
2
2
2
5
2
5
8
5
6
5
3
5
10
5
6
5
5
6
E MSA
bn
n
E MSB
an
n
E MSAB
n
α
αβ
β
αβ
αβ
= σ +
σ
+
σ
=
+
×
×
+
×
=
= σ +
σ +
σ
=
+
×
×
+
×
=
= σ +
σ
=
+
×
=
115
185
35
(b)
What would be the expected mean squares if
2
0
αβ
σ
=
, all other parameters remaining
the same?
(
)
(
)
(
)
2
2
2
2
2
5
2
5
8
5
3
5
10
E MSA
bn
E MSB
an
E MSAB
α
β
= σ +
σ
=
+
×
×
=
= σ +
σ
=
+
×
×
=
= σ
=
85
155
5

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