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3. An experimenter obtained eight yields for the design given below 1 2 3 4 5 Yield 26 28 23 19 18 30 28 Source: Wu & Hamada, Experiments (a) Identify the design in the form of 2R defining relation where Ris the resolution, k is the number of factors, p is the number of basice words in the defining relation. (Hint: Observe that columns 1, 5, and 4 show that it is a 23 full factorial in standard order (Yates order in these three factors. Then, observe how columns 2 and 3 are generated by columns 1,5.) (b) Make two interaction plots for factors 3 and 4, one for 3 against 4, and the other for 4 against 3. (c) Calculate the main effect of 3 and 4 and the 3x4 interaction

(d). If it is known that the standard deviation of each observation is 1.5, what is the standard error of the estimates in (b)?

(e) Based on the results in (a)-(c), which of the three effects in (b) are significant? comment on synergistic and antagonistic interactions.

Please parts (a), (b), (c), (d) & (e). thanks

math   Statistics-And-Probability   
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Answer #1

Sl. No. d=X-Y .4 .6 .427 31 24 25 149 26 26 -2 20 20 30 18 25 Boxplot of d is given below Boxpiot of the differencesQQ plot of the differences Normal Q-a Piat Density plot of the differences density deautx i :Class Interval frequency -10.5)--6.5) -6.5)--25) C-25)-1.5 1.5-5.5 Total 21 30 Histogram of d see that the data given by d doesnot follow normal distribution. If it has foowed normal distribution the points would have lied perfectly on a straight line. But the points were not on a straight line. So,the assumption of normality is not satisfied here

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