An experiment is studied to see whether the travelling time depends either on the routes (Factor A) or the days of the week (Factor B) and the travelling time was recorded and given below. Route (A) 1 2 3 4 1 22 25 26 26 Days of the week (B) 2 3 26 25 27 28 29 33 28 27 The two-factor random effects ANOVA model is given by Xij = μl + ai + Bj + Eij 4 25 26 30 30 S5233 31 29 30

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
Section: Chapter Questions
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3. An experiment is studied to see whether the travelling time depends either on the routes
(Factor A) or the days of the week (Factor B) and the travelling time was recorded and
given below.
Route (A)
1
2
3
4
1
22
25
26
26
Days of the week (B)
2
3
4
5
26
25
25
31
27
28
26
29
29 33
30 33
28 27
30
30
The two-factor random effects ANOVA model is given by
Xij = μ + ai + Bj + € ij
where
μ is the true grand mean, a; is the effect of factor A at level i and ß, is the effect of factor
B at level j.
(a) State the assumptions required for the ANOVA model.
(b) Create an interaction plot and comment on it.
(c) Fit the model using R/Minitab and construct the ANOVA table.
(d) State and test hypotheses appropriate for deciding whether routes has any effect on
travelling time with a = - 5%.
(e) State and test hypotheses appropriate for deciding whether days of the week has any
effect on travelling time with a = 5%.
Transcribed Image Text:3. An experiment is studied to see whether the travelling time depends either on the routes (Factor A) or the days of the week (Factor B) and the travelling time was recorded and given below. Route (A) 1 2 3 4 1 22 25 26 26 Days of the week (B) 2 3 4 5 26 25 25 31 27 28 26 29 29 33 30 33 28 27 30 30 The two-factor random effects ANOVA model is given by Xij = μ + ai + Bj + € ij where μ is the true grand mean, a; is the effect of factor A at level i and ß, is the effect of factor B at level j. (a) State the assumptions required for the ANOVA model. (b) Create an interaction plot and comment on it. (c) Fit the model using R/Minitab and construct the ANOVA table. (d) State and test hypotheses appropriate for deciding whether routes has any effect on travelling time with a = - 5%. (e) State and test hypotheses appropriate for deciding whether days of the week has any effect on travelling time with a = 5%.
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