2. An article by W.D. Baten in the 1956 volume of Industrial Quality Control described an experiment to study the effect of three factors on the lengths of steel bars. Each bar was subjected to one of two heat treatment processes and was cut on one of four machines at one of three times during the day (8 am, 11 am, or 3 pm). The coded length data are shown below Machine Time of Day Heat Treatment Process 1 2 6 9 1 Sam 1 0 -1 0 3 6 7 4 2 4 5 4 7 8 4 3 2 4 0 1 2 0 0 1 4 0 6 1 3 1 5 9 6 3 1 9 3 6 1 3 -1 1 2 4 6 0 7 11am 7 5 6 3 8 4 6 1 10 6 8 10 1 2 5 7 11 9 6 10 4. 4 7 2 - 1 - 1 6 0 4 3 11 4 7 0 1 6 4 3 5 8 3 0 3pm 2 2 -2 -4 (a) Suppose that the observations in the cells are the lengths (coded) of bars processed together in heat treating and then cut sequentially (that is, in order) on the four machines. Analyze the data to determine the effects of the three factors on mean length. (b) Calculate the log variance of the observations in each cell. Analyze the average length and the log variance of the length for each of the 12 bars cut at each machine/heat treatment process combination. What conclusions can you draw? (c) Suppose the time at which a bar is cut really cannot be controlled during routine production. Analyze the average length and the log variance of the length for each of the 12 bars cut at each machine/heat treatment process combination. What conclusions can you draw