a) test for equal variances
Test for Equal Variances: Strength versus Mixture
Method
Null hypothesis | All variances are equal |
Alternative hypothesis | At least one variance is different |
Significance level | α = 0.05 |
Test for Equal Variances: Strength versus slump
Method |
Test Statistic |
P-Value |
Multiple comparisons | — | 0.777 |
Levene | 0.35 | 0.708 |
Test for Equal Variances: Strength vs slump
Method |
Test Statistic |
P-Value |
Multiple comparisons | — | 0.541 |
Levene | 0.38 | 0.688 |
Test for Equal Variances: Strength vs Mixture
requirement of equal variances is provided.
b)
ANOVA test
General Linear Model: Strength versus slump, Mixture
Method
Factor coding | (-1, 0, +1) |
Factor Information
Factor | Type | Levels | Values |
slump | Fixed | 3 | 1, 2, 3 |
Mixture | Fixed | 3 | 1, 2, 3 |
Analysis of Variance
Source | DF | Adj SS | Adj MS | F-Value | P-Value |
slump | 2 | 1179702 | 589851 | 8.60 | 0.002 |
Mixture | 2 | 1760946 | 880473 | 12.83 | 0.000 |
slump*Mixture | 4 | 267304 | 66826 | 0.97 | 0.446 |
Error | 18 | 1235100 | 68617 | ||
Total | 26 | 4443052 |
There is no significant interaction because p -value is more than 0.05.
c) Yes there is a significant difference in three types of mixture.
Yes there is a significant difference in three types of slump.
d)
e)
Tukey Simultaneous Tests for Differences of Means
Difference of Mixture Levels |
Difference of Means |
SE of Difference |
Simultaneous 95% CI |
T-Value |
Adjusted P-Value |
2 - 1 | 626 | 123 | (310, 941) | 5.07 | 0.000 |
3 - 1 | 314 | 123 | (-1, 629) | 2.54 | 0.051 |
3 - 2 | -312 | 123 | (-627, 4) | -2.52 | 0.053 |
Individual confidence level = 98.00%
results indicate that option b is correct.
mixture 67-0-400 is significantly differ from mixture 67-0-301.
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Manufacturer
1
2
3
20
28
20
25
25
18
24
32
24
27
27
18
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