7. Consider the data from Smith and Beverly (1981) taken from a staggered nested design to investigate the sources of variability in impurities in raw materials received at a plant in trailer loads. Two samples of material were taken from each of 9 trailer loads of pellets. Two measurement of impurities was made on the rst sample from each trailer but only on measurement for the second sample from each trailer.

(a) Write the model for the data.

(b) Analyze the data using proc varcomp using the option method=type1 and estimate the three variance components.

(c) Analyze the data using proc varcomp using the option method=reml and check to see if your estimates remain the same.

(d) Make half-normal plots of the square root of the variances pooled to get the mean squares for sample(trailer) and measurement(sample). Does the assumption of homogeneous variances appear reasonable?

(e) Re-analyze the data using proc mixed; calculate the EBLUPs for the random trailer eect and make a normal plot to check the normality assumption. What is your conclusion?

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Table 5.16 Variability in Impurities in Received Pellets Sample 1 2 Measurement Measurement Trailer 1 2 1 12345 47.06 44.37 49.3 47.43 50.35 50.42 3 48.90 48.05 50.64 52.32 52.26 53.47 46.53 45.60 53.98 6 46.99 50.87 51.87 7 47.49 51.55 58.57 8 47.41 47.63 48.63 9 48.37 51.03 50.15 10 54.80 54.80 51.57 54.52