An industrial psychologist working for a large corporation designs a study to evaluate the effect of background music on the typing efficiency of secretaries. The psychologist selects a random sample of seven secretaries from the secretarial pool. Each subject is exposed to three types of background music: no music, classical music, and hard rock music. The subject is given a standard typing test that combines an assessment of speed with a penalty for typing errors. The particular order of the three experiments is randomized for each of the seven subjects. The results are given here, with a high score indicating a superior performance. This is a special type of randomized complete block design in which a single experimental unit serves as a block and receives all treatments.

a. Write a statistical model for this experiment and estimate the parameters in your model.
b. Are there differences in the mean typing efficiencies for the three types of music? 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.

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Subject Type of Music 23 45 67 No music Hard rock Classical 20 17 24 20 22 25 18 20 18 23 121 22 19 24 20 27 22 24 28 16