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A cement manufacturing company has a packing plant containing a large number of packing machines. To test the consistency of packing perfonnance across machines, three machines (denoted by Mle 1, Mle 2, and Mle 3) were selected from the plant, and 20 bags (each supposed to be of weight 50 lb) were filled in each of the three machines. The data (courtesy of T. Dasgupta) in Table 2.10 indicate the actual weight (in pounds) of each of the 60 bags.

(a) Suppose the interest lies in the comparison of the three chosen machines in the plant. Analyze the data using one-way layout with fixed effects. Your work should include ANOVA and F test.

b) What can you conclude from (a)?

(e) Suppose the three machines were selected randomly from the plant. Rean- alyze the data using one-way random effects model. Your work should include ANOYA, F test, and estimates of variance components.

(d) Find a 95% confidence interval for the mean weight of the bags filled in the plant.

1Bble 2.10

MlC 1

49.89 48.80 49.22 49.34 48.77 48.71 50.06 49.51 49.11 49.98 49.64 48.91 50.30 49.67 50.39 50.18 49.09 48.72 49.46 49.30

Packing Machine Data MlC2

50.69 51.5Q 52.09 50.87 50.69 51.05 51.60 50.69 50.48 51.13 51.16 51.49 50.84 51.11 50.94 51.15 52.12 50.84 50.39 51.48

MlC3

49.36 49.92 49.52 50.22 50.23 49.78 48.67 49.98 50.86 50.51 48.95 49.85 49.49 49.29 49.16 50.07 49.64 49.93 49.68

49.62

16. A cement manufacturing company has a packing plant containing a large number of packing machines. To test the consistency of packing performance across machines, three machines (denoted by MIC 1. MC 2, and MIC 3) were selected from the plant. and 20 bags (each supposed to be of weight 50 lb) were lled in each of the three machines. The data (courtesy of T. Dasgupta) in Table 2.10 indicate the actual weight (in pounds) of each of the 60 bags. (a) Suppose the interest lies in the comparison of the three chosen machines in the plant. Analyze the data using one-way layout with xed effects. Your work should include ANOVA and F test. 'Ihble 2.10 Packing Machine um MC 1 MC 2 MIC 3 49.89 50.69 49.36 48.80 51.50 49.92 49.22 52.09 49.52 49.34 50.87 50.22 48.77 50.69 50.23 48.71 51.05 49.78 50.06 51.60 48.6? 49.51 50.69 49.98 49.11 50.48 50.86 49.98 51.13 50.51 49.64 51.16 48.95 48.91 51.49 49.85 50.30 50.84 49.49 49.67 51.11 49.29 50.39 50.94 49.16 50.18 51.15 50.07 49.09 52.12 49.64 48.72 50.84 49.93 49.46 50.39 49.68 49.30 51.48 49.62 (b) What can you conclude from (a)? (c) Suppose the three machines were selected randomly from the plant. Renn- alyze the data using one-way random effects model. Your work should include ANOVA. F test, and estimates of variance components. (I!) Find a 95% condence interval for the mean weight of the bags lled in the plant