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Problem 3 Use Minitab for this problem An experiment is conducted to determine whether the firing oven temperature affects the mean density of a certain type of brick. Multiple bricks are fired at different oven temperatures and the density is measured. The experiment led to the following data (shown in the order in which it was collected) observation Oven Temperature Brick Densit ft 1900 2000 1800 1800 1950 1950 1900 1950 1900 2000 2000 1900 1950 1900 2000 1900 1900 2000 1900 2000 1800 2000 2000 2000 2000 1800 1900 1800 113.1 164.1 113.7 4 146.7 208.3 89.5 147.1 80.8 115.7 183.6 106.0 137.1 108.5 85.2 94.6 133.7 121.3 104.4 141.5 155.5 126.8 138.3 181.7 142.3 124.3 110.2 108.2 8 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26 27 28 (a) What is the response? What is the factor? How many levels of the factor are used? How many replicates were (b) Test the hypothesis that oven temperature affects the mean density of bricks. Use a 0.05. Does oven temperature affect the density of mean bricks? Yes or No? (c) Which oven temperature(s) maximize the mean brick density? Which oven temperature(s) minimize the mean brick density? Use a 0.05

math   Statistics-And-Probability   
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Welcome to Minitab, press Fl for help MTB > MTB > OneWay: SUBC Response Brick density; SUBC Categorical Oven Temprature SUBC IType 0 SUBC Tukey 5; SUBC Fisher 5 SUBC Dunnett 5 1800: SUBC GMCI; SUBCTGrouping; SUBC TMTest; SUBCGIntPlot; SUBC TMethod; SUBC TFactor SUBC TANOVA SUBC TSummary; SUBCTMeans: SUBC Nodefault 2 ## a) Here oven Temprature is Factor and Brick density is Response varaible , each facror is replicated differently ## 1800 replicate 5 times , 1900 replicate 8 , 1950 replicate 5 and last 2000 replicate 10 times with responses## b) for this we can use one way anova One-way ANOVA: Brick density versus Oven Temprature Method Null hypothesis Alternative hypothesis At least one mean is different Significance level All means are equal a0.05 Equal variances were assumed for the analysis Factor Information Levels Values Factor Oven Temprature 4 1800, 1900, 1950, 2000 Analysis of Variance Source Oven Temprature 3 6900 2299.9 Error Total DF Adj SS Adj MS F-Value P-Value 2.96 0.052 24 18617 775.7 27 25517 ### Conclusion : from anova F statistic value and p value we got, we know that we reject Ho at (1-alpha)*100 percent level of ## significance if p value is less than alpha value here p value is greater than alpha value hence we accept H0 ### that mean all means are same ie oven temparature and Brick density are not significant for given dataModel Summary S R-Sq R-Sq(adj) R-sq(pred) 0 , 00% 27.8514 27.04% 17, 92% Means Oven Temprature NMean StDev 1800 1900 1950 2000 95% CI 5 122.54 19.41 96.83, 148.25) 8 106.41 15.16 86.09, 126.74) 5 145.7 42.3 120.0, 171.4) 10 140.05 30.46 (121.87, 158.23) Pooled StDev-27.8514 ## c) we can use here Tucky pairwise comparison test to find out which temaraure inceases Brick density or which not Tukey Pairwise Comparisons Grouping Information Using the Tukey Method and 95% Confidence Oven rature Mean Grouping 1950 2000 1800 1900 5 145.7 A 10 140.05 A 5 122.54 A 8 106.41 A Means that do not share a letter are significantly differentTukey Simultaneous Tests for Differences of Means SE of of Means Difference Difference Difference of Levels 1900 1800 1950 1800 2000 1800 1950 1900 2000 1900 2000 1950 Adjusted T-Value P-Value 0.742 0.561 0.664 0.089 0.078 0.982 95% CI -16.1 23.2 17.5 39.3 33.6 15.9(-59.9, 27.7) -1.02 17.6 (-25.4, 71.8) 15.3 (-24.6, 59.6) 15.9 -4.5, 83.1) 13.2 -2.8, 70.1) 15.3 (-47.8, 36.4) -0.37 1.32 1.15 2.48 2.55 Individual confidence level-98.90% ### Conclusion : form test here all differences are not significantly because all have p value is greater than alpha value.

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  • Problem 3 An experiment is conducted to determine whether the firing oven temperature affects the mean...

    Problem 3 An experiment is conducted to determine whether the firing oven temperature affects the mean density of a certain type of brick. Multiple bricks are fired at different oven temperatures and the density is measured. The experiment led to the following data (shown in the order in which it was collected) e Minitab for this problem observation Oven Temperature (o Brick Densit 113.1 164.1 113.7 1900 2000 1800 1800 1950 1950 1900 1950 1900 2000 2000 1900 1950 1900...

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