3.54. A textile mill has a large number of looms. Each loom is supposed to provide the same output of cloth per minute. To investigate this assumption, five looms are chosen at random, and their output is noted at different times. The following data are obtained:

(a) Explain why this is a random effects experiment. Are the looms equal in output? Use ( = 0.05.

(b) Estimate the variability between looms.

(c) Estimate the experimental error variance.

(d) Find a 95 percent confidence interval for .

(e) Analyze the residuals from this experiment. Do you think that the analysis of variance assumptions are satisfied?

(f) Use the REML method to analyze this data. Compare the 95 percent confidence interval on the error variance from REML with the exact chi-square confidence interval.

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Loom Output (lb/min) 12345 14.0 14.1 14.2 14.0 14.1 13.9 13.8 13.9 14.0 14.0 14.1 14.2 14.1 14.0 13.9 4 13.6 13.8 14.0 13.9 13.7 5 13.8 13.6 13.9 13.8 14.0