Question: Functionalized styrenes are extremely useful building blocks for organic synthesis

Functionalized styrenes are extremely useful building blocks for organic synthesis and for functional polymers. One of the most general syntheses of styrenes involves the combination of an aryl halide with a vinyl organometallic reagent under catalysis by palladium (Pd) complexes. A study was designed to evaluate the effect of different levels of Pd—0.01, 0.05, 0.1, 0.5, and 1.0 (mol%)—on the yield of vinylboronic acid. The reactions take place in a high-pressure chamber at a temperature of 135°C. There are only three pressure chambers available for a single run of the experimental conditions. The chemists were concerned about the substantial run-to-run variations in the yields produced by new setups of the experiment in the chambers. Thus, it was necessary to block on runs, but with only three chambers, it was not possible to include all five levels of Pd during each run. The yields of vinylboronic acid are given in the following table.
a. Describe by name the type of design used. Verify that the structural conditions of your selected design are satisfied in this study.
b. Is there a difference in the average yields of the five levels of paladium? Justify your answer at the α = .05 level.
c. Was it necessary to include the runs factor in the design and subsequent analysis of the data?
d. Using the residuals, do there appear to be any violations in the conditions needed to run tests of hypotheses in the analysis of variances?
e. Do the levels of paladium appear to produce an important difference in average yields if a difference of 4% in yields is considered important

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