Lightweight aggregate asphalt mix has been found to have lower thermal conductiv

Question

Lightweight aggregate asphalt mix has been found to have lower thermal conductivity than a conventional mix, which is desirable. The article "Influence of Selected Mix De- sign Factors on the Thermal Behavior of Lightweight Aggregate Asphalt Mixes" (Journal of Testing and Evaluation, 2008: 1-8) reported an experiment in which various thermal properties of mixes were determined. Three different binder grades were used in combination with three different coarse aggre- gate contents (%), with two observations made for each such combination, resulting in the conductivity data (W/m.°K) that appears in Table 1. The results of the analysis are summarized in Table 2. (a) Complete the last row and the last column of Table 1. (b) Fill in the missing quantities in Table 2. (c) Use = 0.05. Does there appear to be interaction between the factors? Does conductivity appear to depend on either AsphGr or AggCont? (d) If the interaction between the factors is not significant, we remove the interaction term. Construct the new ANOVA table without interaction effect (Table 3)

Explanation / Answer

The Values have been calcualted with the Help of Minitab- By putting the values in the software in the following format

Value Coarse Content Asphalt Binder Grade

0.835 38 PG58

0.845 38 PG58

0.855 38 PG68

0.865 38 PG68

0.815 38 PG70

0.825 38 PG70

0.822 41 PG58

0.826 41 PG58

0.832 41 PG68

0.836 41 PG68

0.800 41 PG70

0.820 41 PG70

0.785 44 PG58

0.795 44 PG58

0.790 44 PG68

0.800 44 PG68

0.770 44 PG70

0.790 44 PG70

Then steps followed to get the answer which is Stat>Anova>Linear fit Model

The answers obtained are as follows

Analysis of Variance

Analysis of Variance

Coarse Aggregate Content(%) Asphalt Binder grade 38 41 44 X.i PG 58 .835,.845 .822,.826 .785,.795 0.818 PG 68 .855,.865 .832,.836 .790,.800 0.8297 PG 70 .815,.825 .800,.820 .770,.790 b X.j a 0.8227 0.7883 a is the average of all the values in the column with coarse content 38% Value of a=.84 b is the average of all the values in the row with inder Grade as PG 70 Value of b=.803 With Interaction Of Variables Without Interaction of Variables

Analysis of Variance

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value Source DF Adj SS Adj MS F-Value P-Value Coarse Content 2 0.008297 0.004149 54.4 0 Coarse Content 2 0.008297 0.004149 56.06 0 Asphalt Binder Grade 2 0.002089 0.001045 13.7 0.001 Asphalt Binder Grade 2 0.002089 0.001045 14.12 0.002 Error 13 0.000991 0.000076 Coarse Content*Asphalt Binder Grade 4 0.000325 0.000081 1.1 0.414 Lack-of-Fit 4 0.000325 0.000081 1.1 0.414 Error 9 0.000666 0.000074 Pure Error 9 0.000666 0.000074 Total 17 0.011378 Total 17 0.011378

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