A compound is sent to five randomly selected laboratories in the United States for a routine analysis. At each laboratory, four chemists are chosen at random, and each chemist makes three chemical determinations on the compound using the same method of chemical analysis. The object is to study the variation of this method from laboratory to laboratory and also among chemists within each laboratory. The data obtained are as follows:

Laboratory Chemist 12345 2.24 2.44 1.97 2.54 2.44 1

Use a SAS program with proc mixed to answer the following questions:

a. Write the appropriate model for the analysis of these data, stating the effect each term used in the model represents and the assumptions made about these effects.

b. Construct an appropriate ANOVA table including the required Fstatistics, p-values, and expected mean squares.

c. State the two hypotheses of interest for this experiment using the model parameters in part (a). Use the F-statistics and p-values above to make conclusions. Use α = 0.05.

d. Estimate parameters of interest in this experiment. Note that these estimates depend on the outcomes of the hypotheses tested above.