A chemist wants to compare the effects of 5 different washing solutions on the removal of stains. It is believed that th

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A Chemist Wants To Compare The Effects Of 5 Different Washing Solutions On The Removal Of Stains It Is Believed That Th 1 (71.5 KiB) Viewed 31 times

A Chemist Wants To Compare The Effects Of 5 Different Washing Solutions On The Removal Of Stains It Is Believed That Th 2 (81.5 KiB) Viewed 31 times

A Chemist Wants To Compare The Effects Of 5 Different Washing Solutions On The Removal Of Stains It Is Believed That Th 3 (7.93 KiB) Viewed 31 times

A chemist wants to compare the effects of 5 different washing solutions on the removal of stains. It is believed that the washing solutions may work differently on various types of fabric. Five types of fabric were therefore considered, where the solutions were randomly applied to a common stain on each fabric. The values of the strength index are recorded in the table below. Fabric 3 2 68 67 74 Solution 1 2 3 4 5 1--以以四段 4乃乃乃 5 67 70 68 72 72 73 76 73 73 75 73 77 71 75 78 75 69 i) Determine if the design above is balanced. The code below was run with the data above in the statistical software R. The following results are obtained. Note that some information has been removed. > modell = lm (Strength Solution + Fabric) > anova (modell) Analysis of Variance Table Response: Strength DE Sum sa Mean Sq F value Solution 4 105.00 26.2500 11.7617 Fabric 4 78.20 19.5500 8.7597 Residuals 11 24.55 2.2318 Pr (>F) * REMOVED* *** * REMOVED* ** Fabric + Solution) > model2 = lm (Strength > anova (model 2)
Analysis of Variance Table Response: Strength DE Sum Sa Fabric 4. 116.00 Solution 4 67.20 Residuals 11 24.55 Mean Sq 29.0000 16.8000 2.2318 F value 12.9939 7.5275 Pr (>F) * REMOVED* *** * REMOVED* ** ii) Identify the treatments and the blocking variable. Hence state the values of MST radjusted and MSB Adjusted iii) What is the appropriate F value for the variable Solution? Using (iii) test the significance of Solution at a 5% level of significance. State your hypotheses clearly. iv) v) What is the appropriate F value for the variable Fabric? Can this F-value be used to test any hypotheses? Explain why or why not. What conclusions can you make from this F-value? 1 A Least-Squares means test is further performed in R with results as follows. > lsm Ismeans (model2, specs="Solution") > pairs (sm) contrast estimate SE df t.ratio p.value 1 2 -1.067 1.09 11 -0.978 0.8598 3 -1.667 1.09 11 -1.528 0.5671 1 4 -5.600 1.09 11 -5.133 0.0024 1 5 -2.000 1.09 11 -1.833 0.4034 2 3 -0.600 1.09 11 -0.550 0.9797 2 4 -4.533 1.09 11 -4.155 0.0111 5 -0.933 1.09 11 -0.855 0.9071 4 -3.933 1.09 -3.605 0.0272 5 -0.333 1.09 11 -0.306 0.9978 4 5 3.600 1.09 11 3.300 0.0449 си в сиво от Б N N الما 11 لما 4 - vi) What are the general hypotheses tested in a Least-Squares means test?
vii) From the pairs (1sm) output given, what are your conclusions? Use a significance level of a = 0.05. [5+4+1+4+4+1+3]