a) Appropriate test statistic: Two-way
ANOVA
Output using excel:
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Anova: Two-Factor With Replication |
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SUMMARY |
One
hour |
Two
hour |
Three
hour |
Total |
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Old |
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Count |
3 |
3 |
3 |
9 |
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| Sum |
18 |
20 |
27 |
65 |
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Average |
6 |
6.666667 |
9 |
7.222222 |
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Variance |
1 |
0.333333 |
1 |
2.444444 |
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Meaningful |
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Count |
3 |
3 |
3 |
9 |
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| Sum |
24 |
30 |
26 |
80 |
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Average |
8 |
10 |
8.666667 |
8.888889 |
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Variance |
7 |
1 |
2.333333 |
3.361111 |
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Total |
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Count |
6 |
6 |
6 |
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| Sum |
42 |
50 |
53 |
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Average |
7 |
8.333333 |
8.833333 |
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Variance |
4.4 |
3.866667 |
1.366667 |
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ANOVA |
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Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
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Sample |
12.5 |
1 |
12.5 |
5.921053 |
0.031541 |
9.330212 |
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Columns |
10.77778 |
2 |
5.388889 |
2.552632 |
0.119209 |
6.926608 |
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Interaction |
10.33333 |
2 |
5.166667 |
2.447368 |
0.128404 |
6.926608 |
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Within |
25.33333 |
12 |
2.111111 |
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Total |
58.94444 |
17 |
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b) Train:
p-value = 0.0315
Decision:
As p-value > 0.01, we fail to reject Ho
------------------
Time:
p-value = 0.1192
Decision:
As p-value > 0.01, we fail to reject Ho
-------------------
Interaction:
p-value = 0.1284
Decision:
As p-value > 0.01, we fail to reject Ho
