H
0
:
μ
1
=
μ
2
=
μ
3
=
μ
4
,
where
μ
j
= the average time required to fill Form
j
.
H
a
:
at least two of
μ
j
’s are different.
OR
H
0
:
τ
1
=
τ
2
=
τ
3
=
τ
4
= 0.
H
a
:
Not
H
0
.
(ii)
The time required to fill Form
j
is normally distributed with mean
μ
j
and common
variance
σ
2
,
j
= 1, 2, 3, 4.
Our data are four independent random samples from these
four populations.
Y
i
j
=
μ
j
+
ε
i
j
,
i
= 1, 2, … , 30,
j
= 1, 2, 3, 4,
where
ε
i
j
’s
are
i.i.d.
N
(
0,
σ
2
).
OR
Y
i
j
=
μ
+
τ
j
+
ε
i
j
,
i
= 1, 2, … , 30,
j
= 1, 2, 3, 4,
where
ε
i
j
’s
are
i.i.d.
N
(
0,
σ
2
),
∑
=
4
1
τ
j
j
=
0.
(iii)
> Hw02_1 <- read.table("http://www.stat.uiuc.edu/~stepanov/Hw02_1.csv", sep=",", header=T)
> Time <- c(Hw02_1$Form1, Hw02_1$Form2, Hw02_1$Form3, Hw02_1$Form4)
> Form <- c(rep(1,30), rep(2,30), rep(3,30), rep(4,30))
> summary(aov(glm(Time ~ factor(Form))))
Df Sum Sq Mean Sq F value
Pr(>F)
factor(Form)
3
8464
2821
2.9358 0.03632 *
Residuals
116 111480