In the book Bayesian Inference in Statistical Analysis (1973, John Wiley and Sons) by Box and Tiao, the total product yield for five samples was determined randomly selected from each of six randomly chosen batches of raw material.

(a) Do the different batches of raw material significantly affect mean yield? Use α = 0.01.

(b) Estimate the variability between batches.

(c) Estimate the variability between samples within batches.

(d) Analyze the residuals from this experiment and check for model adequacy.

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Yield (in grams) Batch 1545 1440 1440 1520 1580 1555 2 1540 1490 1560 1495 1560 3 1595 1550 1605 1510 1465 1445 1440 1595 1545 1515 1595 1630 1635 1625 6. 1520 1455 1450 1480 1445