The following data give the amount, in parts per million (ppm), of a toxic substance as measured by four randomly selected laboratories. Each laboratory made six measurements of the toxic substance.

The following data give the amount, in parts per million (ppm), of a toxic substance as measured by four randomly selected laboratories. Each laboratory made six measurements of the toxic substance. The question to be studied was how much of the variability is due to the different laboratory techniques and how much is due to random error.

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(Source: J.S. Milton and J.C. Arnold, Introduction to Probability and Statistics, 2nd ed., McGraw–Hill.) (a) Explain why the random effects model is appropriate. (b) Construct the appropriate ANOVA , and test at the level α = 0.05 the null hypothesis that there is no significant differences in the toxic levels as measured by the different laboratories. (c) Estimate the variance components.

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