Question

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I am trying to solve the questions using Minitab. I need the answer in 12 hours. Please provide answer with Minitab steps.

A 23 factorial experiment is conducted to determine the main effects and interactions among 3 factors (presence/absence) on taste quality for frozen dinners. The following table gives the design, mean, and standard deviation (SD) for the 8 combinations of factor levels. There were 4 replicates per treatment. -1 -1 (1) a b c 1 -1 -1 1 1 -1 1 - 1 -1 1 1 -1 1 -1 -1 -1 1 - 1 1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 40 2 50 3 42 1 38 2 532 ab | -1 1 -1 1 1 1 ac 1 -1 47 -1 -1 1 1 bc abc | 1 1 1 3 2 50 1. Give the +17-1 levels for the ABC Interaction. 2. Compute SSA 3. Test the Hypothesis of the effect of factor A. 4. Can you compute SST, if yes, compute ANOVA table, and determine the significant factors, and their interactions? 5. Compute the regression model coefficients to predict the output. 6. Test the model assumption (residuals normality , constant variance ...)

Answer 1

from the Given table : We Calculate following Table treatment T factorial (0 Effect | + - of signe for Factorial effects in terms of mean for 23. design O Treatment (a) (b) cab) (c) (ac) (c) (abe) divisible + + + + + + + + - + - + - + - + + - - - - + - - + + - - + - - * - at t - - + + + + + i II t t t l + + + IIII + + AB + + i 1 AC + 1 + + LC + ABC 1 + t I + (") +1/4 levels for the ABC interaction is - - + + + + - + - - 1, +, -1,- + +, © Compute SSA. Son of Sum square due to treatment for Main effects. A > SA² =[A]² 50 = 78.925 BS SB² = [ csscanned with CamScanner 32 55.12

1444 - 5125 C-607** (4.69*. 4493 1.5125 32 AB 2009 07.78 32 32 64.03 - 2207 32 BC 1600 - 50 32 32 32 ne (AL= (*** = 2202 = 64-03 BC - (cel(909% = = 50 ABC > (960)*. 2500 70-125 ② Hypothesis for factor A: 32 factor A. Ho : Trestment are homogeneous as were as blocks[4]. Now for effect A. 5.5 (A) = 78-925 of Mus.(A] = 78-925 278-925 (1. do ff] Sos (Estor) – 36. degree of freedom for error =(n-1) (2²_1) = 3 x = 2! Mis (Essor] - 34 =1-23 so so F = 78.925 -64016 123 F[tabulated) at .05,1,2) = 4:32. as Calculated > Tabulated C Scanned with cascamereject Noll hypothesis

ANOVA Table for 23. Factorial Experiment. Tabulate Siv dif 1 s. s I Miss L Miss Tlm. s. el Dirty Replicate 3 - Treatment 17 2.57 6 64.085 78.925 55-12 66.297 76.925 55:12 4.32 -- 30.675 46.04 36.15 50-44 26.32 40-27 4.32 4-32 87. 78 67.78 45.125 450125 69.03 69.03 4-32 4.32 4-2 29.17 50. ---- all 50 78.125 45:58 4032 76. 125 ABC Sic 36 je 714 Total As all Calculated value than tabulated value That mean we reject of so our treatment is greater all testment are significant- Null hypothesis. and all effect are significant Regression model 2² design If lifke is the response observed at the level of A, the level of R kith level of G in the ith replicate, then the linear moder for 22 experiment Yogkl = Metaq 4 Bj + 8 + (af) is +(188) jk + CSScanned with CamScanner (ABV) ik + fx +Eike