Suppose that, when setting up his experiment in Problem 11.54, the operations manager had access to only six samples of yarn from the batch but was able to divide each yarn sample into three parts and randomly assign them, one each, to the three air-jet pressure levels. Thus, instead of the one-factor completely randomized design model in Problem 11.54, he used a randomized block design with the six yarn samples being the blocks and one yarn part each assigned to the three air-jet pressure levels. The breaking- strength scores are stored in Yarn.
a. At the 0.05 level of significance, is there evidence of a difference in the mean breaking strengths for the three air-jet pressures?
b. If appropriate, use the Tukey procedure to determine the air-jet pressures that differ in mean breaking strength. (Use α = 0.05.)
c. At the 0.05 level of significance, is there evidence of a blocking effect?
d. Determine the relative efficiency of the randomized block design as compared with the completely randomized design.
e. Compare your result in (a) with your result in Problem 11.54 (b). Given your results in (c) and (d), what do you think happened? What can you conclude about the "impact of blocking" when the blocks themselves are not really different from each other?