An engineer wants to know if the mean strengths of three different concrete mix designs differ significantly. He also suspects that slump may be a predictor of concrete strength. Slump is a measure of the uniformity of the concrete, with a higher slump indicating a less uniform mixture. The following data represent the 28-day strength (in pounds per square inch) of three different mixtures with three different slumps.

(a) Normal probability plots indicate that it is reasonable to believe that the data come from populations that are normally distributed. Verify the requirement of equal population variances.
(b) Determine whether there is significant interaction between mixture type and slump.
(c) If there is no significant interaction, determine whether there is significant difference in the means for the three types of mixture. If there is no significant interaction, determine whether there is significant difference in the means for the slumps.
(d) Draw an interaction plot of the data to support the results of parts (b) and (c).
(e) The residuals are normally distributed. Verify this.
(f) If there is significant difference in the means for the three mixture types, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05. If there is significant difference in the means for the slumps, use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.

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Mixture Mixture Mixture Slump 67-0-301 67-0-400 67-0-353 3.75 3960 4815 4595 4005 4595 4145 3445 4185 4585 4 4010 4070 3855 3415 4545 3675 3710 4175 4010 3290 4020 3875 3390 4355 3700 3935 3740 3350