Paint used for marking lanes on highways must be very durable. In one experiment
ID: 3152696 • Letter: P
Question
Paint used for marking lanes on highways must be very durable. In one experiment, paint from four different suppliers, labeled GS, FD, L, and ZK, were tested on six different highway sites, denoted 1, 2, 3, 4, 5, and 6. After a considerable length of time, which included different levels of traffic and weather, the average wear for the samples at the six sites was as follows (i.e., a bigger number means more wear):
Paint Supplier
Site
GS
FD
L
ZK
1
69
59
55
70
2
83
65
65
75
3
74
64
59
74
4
61
52
59
62
5
78
71
67
74
6
69
64
58
74
The FD and L paints are more expensive paints and are expected to have better wear properties than the less expensive GS and ZK paints.
a) Conduct an appropriate ANOVA using the two-way ANOVA, additive model in Excel.
b) Construct a scaled-t reference distribution to compare treatment means. Clearly show your work. Interpret your results.
c) Construct all pairwise comparisons using a = 0.01. Interpret your results.
Paint Supplier
Site
GS
FD
L
ZK
1
69
59
55
70
2
83
65
65
75
3
74
64
59
74
4
61
52
59
62
5
78
71
67
74
6
69
64
58
74
Explanation / Answer
H0: All the treatment means are equal
H1: Atleast one tereatment mean is not equal to zero
alpha:1% level
Test statistic:
From Excel
F cal= 10.459
Conclsuion: P value=0.000018 < 0.01 we reject the H0. Hence the claim is signifiant
Now for BLOCKS:
Null hypothesis: All the blocks means are equal
alternative hyp: Alteast one block mean is not equal
alpha:1%
Test statistic:
F cal=20.39
Conclusion:
P value=0.000015 <0.01 we reject the null hypothesis. Hence the claim is significant
Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance 1 4 253 63.25 54.91667 2 4 288 72 76 3 4 271 67.75 56.25 4 4 234 58.5 20.33333 5 4 290 72.5 21.66667 6 4 265 66.25 46.91667 GS 6 434 72.33333 59.86667 FD 6 375 62.5 41.1 L 6 363 60.5 20.7 ZK 6 429 71.5 24.7 ANOVA Source of Variation SS df MS F P-value F crit Rows 568.7083 5 113.7417 10.459 0.000181 4.555614 Columns 665.125 3 221.7083 20.38697 1.5E-05 5.416965 Error 163.125 15 10.875 Total 1396.958 23Related Questions
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