IME 326- Homework 9

IME 326- Homework 9 - Megan Farrell IME 326-02 March 3,...

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Megan Farrell IME 326-02 March 3, 2011 Homework #8 Problem 1 : 1) Null Hypothesis: Adding various glass sizes and particle content to clay bricks makes no difference in the structural properties of the brick. Alternative Hypothesis: Adding various glass sizes and particle content to clay bricks makes an improvement in the structural properties of the brick. 2) Minitab was used to calculate the ANOVA table and all the plots, as seen in the next steps. 3) ANOVA Table Source DF SS MS F P Size 1 2110.1 2110.09 14.86 0.001 Glass Content 2 6890.1 3445.07 24.26 0.000 Interaction 2 2201.3 1100.67 7.75 0.003 Error 24 3408.1 142.01 Total 29 14609.7 4) Plots of Effects
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5) Conclusion: Because the P-value was less than 0.05 in both the size level, glass content level, and the interaction effect, one can reject the null hypothesis in all three cases, as all three factors were statistically significant and played a role in the structural properties of the brick. 6) Interpretation: The structural properties of the brick are influenced by adding glass in various contents and sizes. The strength of the brick increased when adding fine glass opposed to coarse glass and when glass made up 15% instead of %5 or 10%. In addition, the interaction between the adding more glass, of finer particles and coarse particles, greatly increased the strength than just one of the factors by itself, as seen in the Interaction Plot. 8) A Tukey Test must be performed because we can reject the null hypothesis for all three factors. Below are the Minitab outputs for the Tukey Comparison Test. Grouping Information Using Tukey Method and 95.0% Confidence Size N Mean Grouping Fine 15 99.9 A Coarse 15 83.1 B Means that do not share a letter are significantly different. Tukey 95.0% Simultaneous Confidence Intervals Response Variable Strength All Pairwise Comparisons among Levels of Size Size = Coarse subtracted from: Size Lower Center Upper +---------+---------+---------+------ Fine 5.749 16.77 27.80 (-----------------*-----------------) +---------+---------+---------+------ 6.0 12.0 18.0 24.0 Grouping Information Using Tukey Method and 95.0% Confidence Glass Content N Mean Grouping 15 10 112.9 A 10 10 81.6 B
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5 10 80.0 B Means that do not share a letter are significantly different. Tukey 95.0% Simultaneous Confidence Intervals Response Variable Strength All Pairwise Comparisons among Levels of Glass Content Glass Content = 5 subtracted from: Glass Content Lower Center Upper -------+---------+---------+--------- 10 -14.74 1.560 17.86 (-------*-------) 15 16.60 32.900 49.20 (-------*--------) -------+---------+---------+--------- 0 20 40 Glass Content = 10 subtracted from: Glass Content Lower Center Upper -------+---------+---------+--------- 15 15.04 31.34 47.64 (-------*-------) -------+---------+---------+--------- 0 20 40 This Tukey Test shows that the fine and coarse sizes are significantly different while the 15% glass content is significantly different from the 5% and 10%, but the 5% and 10%
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IME 326- Homework 9 - Megan Farrell IME 326-02 March 3,...

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