A manufacturer suspects that the batches of raw material furnished by his supplier differ significantly in calcium content. There are a large number of batches currently in the warehouse. Five of these are randomly selected for study. A chemist makes five determinations on each batch and obtains the following data: 

 

(a) Is there significant variation in calcium content from batch to batch? Use α = 0.05.

(b) Estimate the components of variance.

(c) Find a 95 percent confidence interval for σ_τ(σ²_τ + σ²).

(d) Analyze the residuals from this experiment. Are the analysis of variance assumptions satisfied?

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Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 23.46 23.59 23.51 23.28 23.29 23.48 23.46 23.64 23.40 23.46 23.56 23.42 23.46 23.37 23.37 23.39 23.49 23.52 23.46 23.32 23.40 23.50 23.49 23.39 23.38