An experiment was conducted to monitor the resistivity of silicon mono crystals. The original data were collected according to a two-stage nested sampling design in which random samples of eight crystals were selected from among 30 lots. The measured resistivity of the crystals is recorded in the accompanying table for five of these lots.
a. Construct an ANOVA summary table for the nested design.    

b. Let σ_B² and σ_W² represent the components of between and within-lot variances, respectively, of the resistivity readings. Obtain the estimates of σ_B² and σ_W².
c. Do the data provide sufficient evidence to indicate that the variation in resistivity between lots exceeds the variation within lots? Test using α = .05.

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CRYSTALS Lot Measured values of Resistivity 1 2.8 2.7 2.3 2.6 2.7 2.3 2.7 2.7 3.0 3.0 2.8 2.4 3.0 3.2 2.9 2.4 2.4 2.3 2.4 2.9 2.4 2.4 2.3 2.3 4 3.1 2.9 3.0 3.0 2.6 3.0 2.9 3.0 3.1 3.3 2.9 2.5 2.5 3.1 2.5 3.0 3. 5.