A quality control engineer is considering implementing a workshop to instruct workers on the principles of total quality management ( TQM). The program would be quite expensive to implement across the whole corporation; hence, the engineer has designed a study to evaluate which of four types of workshops would be most effective. The response variable will be the in­crease in productivity of the worker after participating in the workshop. Since the effectiveness of the workshop may depend on the worker€™s preconceived attitude concerning TQM, the workers are given an examination to determine their attitudes prior to taking the workshop. Their attitudes are classified into five groups. There are four workers in each group, and the type of workshop is randomly assigned to the workers within each group. The increases in productivity are given here.

a. Write a statistical model for this experiment, and estimate the parameters in your model.
b. Are there differences in the mean increases in productivity for the four types of workshops? Use α = .05.
c. Does the additive model for a randomized complete block design appear to be appropriate?
d. Compute the relative efficiency of the randomized block design compared to a completely randomized design. Interpret this value. Were the blocks effective in reducing the variability in experimental units? Explain.

Attitude Type of Workshop 2 38 37 42 5 Mean 42 47 42 52 54 50 55 62 42.8 46.6 50.6 61.0 39 43 62 71 74 84 35 40 Mean 40.5 41.75 45.5 50.757275 50.25