Refer to the randomized block design setup to compare the mean costs estimated by four DOT engineers, Examples 13.2 and 13.3.

a. Write the model for each observation of estimated cost y for engineer B. Sum the observations to obtain the average for engineer B.

b. Repeat part a for engineer D.

c. Show that (y̅_B - y̅_D) = β₂ + (ɛ̅_B - ɛ̅_D) Note that the β’s for blocks cancel when computing this difference.

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Example 13.2 Suppose you want to compare the abilities of four Department of Transportation (DOT) engineers, A, B, C, D, to estimate the cost of road construction contracts. One way to make the comparison would be to randomly allocate a number of road contracts-say, 40–10 to each of the four DOT en- gineers. Each engineer would then estimate the cost y of each contract. The treatment allocation to experimental units that we have described is a completely randomized design. Noise-Reducing Design: Engineer Cost Estimation a. Discuss the problems that result when the completely randomized design is used for this experiment. b. Explain how you would employ a randomized block design.