1. IN MINITAB: The following data represents the strength of a certain wrapper representing two levels of each of four process variables (A,B,C,D). An operator effect was introduced into the model since it was necessary to obtain half of the runs under operator 1 and half under operator 2. (a) Manually in excel: Using the Kempthone i.e. MOD method (Modulo 2 operator), show that ABC was confounded with operators. (b) Assuming all 3-way and 4-way interactions are negligible, create the confounded factorial design, and carry out the significance tests for the four factors and their 2-way interactions (c) Can the design be reduced further? Support your answer from the AVOVA solutions. The data is as follows: Operator 1: (1)=18.8, d=13.5 ab=16.5, abd=17.6, ac=17.8, acd=18.5, bc=17.3 bcd=17.6 Operator 2: a=14.7 ad=16.9 b=15.1 bd=17.5 c=14.7 cd=18.2 abc=19.0 abcd= 20.1 2. IN MINITAB: An experiment was conducted to study the yield of an isatin derivative prepared from base material. The factors studied were: Acid strength (A), Time (B), Laboratory (C), Temperature (D) and amount of acid (E) (a) Analyze the data assuming that 2nd order and higher interactions are negligible. Indicate all significant effects. (b) Suppose a quarter fraction of the design could be run. Construct the design and analyze the data using the defining contrast as (BCE and ADE) show all aliases and the final ANOVA. (c) Look up the generator for this design that would produce the best resolution. Repeat the analysis with this better resolution design and comment on the difference or similarities between the ANOVA results in c and d. Do you think the choice of generator changed the conclusions from the experiment? A1 A2 B1 D1 D2 B2 B1 B2 C1 C2 C1 C2 C1 C2 C1 C2 E1 7 6 34 30 9 10 55 50 E2 8 5 35 25 12 12 62 55 E1 10 8 30 34 11 11 61 60 E2 10 15 40 34 15 20 65 65 1 3. The following are the measurements of the elevation (Y) of a straight (but hilly) bikers’ route above a fixed reference point, made at increasing horizontal distances (X) along the route. a) Produce a line plot of the elevation against the distance. What kind of relationship seems to be evident? b) IN MS EXCEL: Consider it as a single-factor experiment with 10 levels i.e. 0,1,…,9. Using the ORTHOGONAL POLYNOMIAL Contrast Method, test the significance of the 1st, 2nd, 3rd, and 4th order terms. c) What terms should be included in the regression model? (Ensure that the principle of Hierarchy is followed i.e. if the quadratic term is insignificant and the cubic term is significant, the regression should have the linear, quadratic and cubic terms). d) Carry out the regression model (in MINITAB) with the required terms and estimate the regression equation. e) Using the regression, estimate the elevations at the 10 levels of distance and produce a line plot of the estimated distances. f) What are the lowest and the highest points of the bikers’ route? Use the results to estimate the location of the crest of the hill and the bottom of the dip based on at  = 0.05 Y =Elevation (ft) 0 6 12 19 16 9 10 11 15 20 X= Distance (100 ft) 0 1 2 3 4 5 6 7 8 9 2