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STA2020F 2007
CLASS TEST 1 SOLUTIONS
SECTION A:
1.
T
2.
F
3.
T
4.
T
5.
T
6.
T
7.
T
8.
F
[1 x 8 = 8]
SECTION B:
Question 1:
[13]
a.
Two factor anova with interaction or two factor factorial experiment
[1]
b.
Variation due to differences in room sizes (density) [2]; Variation due to
differences in behaviour (Comments) [2]; Variation due to interaction between
behaviour (Comments) [2] and room sizes (Density) [2]; Variation due to error
[2]; Total Variation [2].
c.
(i)
Separate studies cannot reveal interaction between the two factors [1]
(ii)
A factorial design is economical in that in a single experiment one can
study the effects of the main factors and that of interaction.
[1]
Question 2:
[12]
a.
0
1
2
3
:
H
μ
=
=
1
H
:
at least 2 means differ
(2)
b.
Source of Variation
SS
df
MS
F
F critical
Treatments
36.4
2
18.2
5.2
3.89
Error
42.0
12
3.5
Total
78.4
14
(8)
c.
Test statistic:
F
= 5.2; Critical value, F
2, 12
= 3.89.
Since
F
= 5.2 > 3.89, reject
0
H
. Therefore at least two of the population means differ.
(2)
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View Full DocumentQuestion 3.
[12]
(a)
Complete 3 x 3 factorial experiment. [1]
(b)
SS(AB) measures the variability in share price between combinations
(interactions) of the levels of the two factors. [2]
(c)
(i)
H
0
: The levels of the two factors do NOT interact to affect the mean
share
price
H
1
: The levels of the two factors interact to affect the mean share price
[1]
F
STAT
= 1.8898
Pvalue = 0.1202
Since the pvalue of 0.1202 > 0.05, we do NOT reject H
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 Three '09
 JAMES

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