The article &ldquo;Anodic Fenton Treatment of Treflan MTF&rdquo; describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the (displaystyle{F}{e}^{{{2}}} : {H}_{{{2}}} {O}_{{{2}}}) delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. (begin{array}{|c|c|}hline text{Initial Concentration (M)} &amp; text{Delivery Ratio} &amp; text{Sorption (%)} hline 15 &amp; 1:0 &amp; 10.90 quad 8.47 quad 12.43 hline 15 &amp; 1:1 &amp; 3.33 quad 2.40 quad 2.67 hline 15 &amp; 1:5 &amp; 0.79 quad 0.76 quad 0.84 hline 15 &amp; 1:10 &amp; 0.54 quad 0.69 quad 0.57 hline 40 &amp; 1:0 &amp; 6.84 quad 7.68 quad 6.79 hline 40 &amp; 1:1 &amp; 1.72 quad 1.55 quad 1.82 hline 40 &amp; 1:5 &amp; 0.68 quad 0.83 quad 0.89 hline 40 &amp; 1:10 &amp; 0.58 quad 1.13 quad 1.28 hline 100 &amp; 1:0 &amp; 6.61 quad 6.66 quad 7.43 hline 100 &amp; 1:1 &amp; 1.25 quad 1.46 quad 1.49 hline 100 &amp; 1:5 &amp; 1.17 quad 1.27 quad 1.16 hline 100 &amp; 1:10 &amp; 0.93 quad 0.67 quad 0.80 hline end{array}) a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.

Question

The article &amp;ldquo;Anodic Fenton Treatment of Treflan MTF&amp;rdquo; describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the (displaystyle{F}{e}^{{{2}}} : {H}_{{{2}}} {O}_{{{2}}}) delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. (begin{array}{|c|c|}hline text{Initial Concentration (M)} &amp;amp; text{Delivery Ratio} &amp;amp; text{Sorption (%)}  hline 15 &amp;amp; 1:0 &amp;amp; 10.90 quad 8.47 quad 12.43  hline 15 &amp;amp; 1:1 &amp;amp; 3.33 quad 2.40 quad 2.67  hline 15 &amp;amp; 1:5 &amp;amp; 0.79 quad 0.76 quad 0.84  hline 15 &amp;amp; 1:10 &amp;amp; 0.54 quad 0.69 quad 0.57  hline 40 &amp;amp; 1:0 &amp;amp; 6.84 quad 7.68 quad 6.79  hline 40 &amp;amp; 1:1 &amp;amp; 1.72 quad 1.55 quad 1.82  hline 40 &amp;amp; 1:5 &amp;amp; 0.68 quad 0.83 quad 0.89  hline 40 &amp;amp; 1:10 &amp;amp; 0.58 quad 1.13 quad 1.28  hline 100 &amp;amp; 1:0 &amp;amp; 6.61 quad 6.66 quad 7.43  hline 100 &amp;amp; 1:1 &amp;amp; 1.25 quad 1.46 quad 1.49  hline 100 &amp;amp; 1:5 &amp;amp; 1.17 quad 1.27 quad 1.16  hline 100 &amp;amp; 1:10 &amp;amp; 0.93 quad 0.67 quad 0.80 hline end{array}) a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.

Bentley Leach · Accepted Answer

Step 1 Given: I=3 J=4 K=3 a) The mean is the sum of all values divided by the number of data values: X―1.=3.6992 X―2.=2.6492 X―3.=2.575 X―.1=8.2011 X―.2=1.9656 X―.3=0.9322 X―.4=0.7989 X―11=10.6 X―12=2.8 X―13=0.7967 X―14=0.6 X―21=7.1033 X―22=1.6967 X―23=0.8 X―24=0.9967 X―31=6.9 X―32=1.4 X―33=1.2 X―34=0.8 X―=2.9744 Step 2 The main effects are the difference of the mean of the values in the category decreased by the overall mean. Main effects concentration X―1. − X―=3.6992 − 2.9744=0.7248 X―2. − X―=2.6492 − 2.9744= −0.3252 X―3. − X―=2.575 − 2.9744= −0.3994 Main effects delivery ratio X―.1 − X―=8.2011 − 2.9744=5.2267 X―.2 − X―=1.9656 − 2.9744= −1.0088 X―.3 − X―=0.9322 − 2.9744= −2.0422

The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin.

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