Two missing values in a randomized block. Suppose that in Problem 4-1 the observations for chemical type 2 and bolt 3 and chemical type 4 and bolt 4 are missing.

(a) Analyze the design by iteratively estimating the missing values, as described in Section 4-1.3. 

(b) Differentiate SSE with respect to the two missing values, equate the results to zero, and solve for estimates of the missing values. Analyze the design using these two estimates of the missing values.

(c) Derive general formulas for estimating two missing values when the observations are in different blocks.

(d) Derive general formulas for estimating two missing values when the observations are in the same block.

Problem 4-1

A chemist wishes to test the effect of four chemical agents on the strength of a particular type of cloth. Because there might be variability from one bolt to another, the chemist decides to use a randomized block design, with the bolts of cloth considered as blocks. She selects five bolts and applies all four chemicals in random order to each bolt. The resulting tensile strengths follow. Analyze the data from this experiment (use α = 0.05) and draw appropriate conclusions. 

 

Transcribed Image Text:

Bolt Chemical 1 3 4 1 73 68 74 71 67 2 73 67 75 72 70 75 68 78 73 68 4 73 71 75 75 69 2.