Question 3 [45 points]: Nanosized titanium dioxide (TiO2) photocatalytic papers

Question

Question 3 [45 points]: Nanosized titanium dioxide (TiO2) photocatalytic papers can be prepared using a natural zeolite microparticle retention aid in papermaking. These photocatalytic papers might be used for environmental purification. Multiple factors are involved here which are the % natural zeolite, the % cationic starch and the % cationic polyacrylamide. A factorial experimental design was done to study the effects of these factors for increasing the TiO2 retention rate in paper stock. The three factors mentioned above and their levels are shown in the following table: Factor Symbol Variable Levels % Natural zeolite % cationic starch % Cationi? polyacrylamide l 0 0 0.5 The P-values for the different factors are assumed to be as shown in the following table which is also available in the LSSGB FinalExam_Summer 2018.xls Excel file Factor Degrees of Freedom |Sequential SS Adjusted SS Adjusted MS F P-value 0.20 0.23 0.18 0.56 0.45 0.63 0.201 0.23 0.18 0.566 0.451 0.632 0.201 0.233 0.18 0.56 0.451 0.63 30 0 2.030.1 15 0.08 1.300.4 1.900.12 22.030.03 AxBI1 AxC1 BxC1 The main and interaction plots are shown below:

Explanation / Answer

1)

There are three factors tested each with two levels. These factors are,

2)

A factor is called significant if its p-value is less than the significance leve. The p-value for each factor is given below,

From the above comparison only factor A and B*C have p-value less than 0.05 at 5% significance level. Hence only factor A and the interaction of B and C have significant effect on dependent variable.

iii)

From plot (A)

There is a large variation in factor A when moving from level one to two. This shows a main effect of factor A while factor B and factor doesnot have such large variation when moving from level one to two.

From plot (B)

The parallel line shows that there is no interaction while the non parallel shows the presence interaction between factor. Here factor B and C has a non parallel lines which shows an interaction. While A and B have roughly parallel line hence no interaction. Here plot of A and C show an interaction because of non parallel line.

4)

From the regression analysis it show factor A and interaction of B and C have a significant effect on dependent variable. And from the main and interaction plot it also the main effect of factor A and inteaction of B and C but from the plot analysis it also shows the interaction between A and C.

Levels Factor A 0 and 2 Factor B 0 and 0.5 Factor C 0 and 0.1

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