Each of three chemical laboratories performed four replicate determinations of the concentration of suspended particulate matter in a certain area using the "Hi-Vol" method of analysis. The resulting data are presented next.

a. Identify the appropriate ANOVA table for these data.
b. Test the null hypothesis of no differences among the laboratories.
c. With large-scale interlaboratory studies, analysts usually make inferences about a large population of laboratories of which only a random sample (e.g., laboratories I, II, and III) can be investigated. In such a case, describe the appropriate random-effects model for the data.
d. Two quantities of particular interest in a large-scale interlaboratory study are repeatability (i.e., a measure of the variability among replicate measurements within a single laboratory) and reproducibility (i.e., a measure of the variability between results from different laboratories). Using the random-effects model defined in part (c), define what you think are reasonable measures of repeatability and reproducibility, and obtain estimates of the quantities you have defined using the data in the accompanying computer output.

Lab 1 Lab II Lab III 10 Dependent Variable: conc Pr> F 1.75 02280 F Value Source Model Error Corrected Total DF Sum of Squares Mean Square 18.66666867 48 00000000 66.66666667 9.33333333 5.33333333 11 R-Square Coeff Var Root MSE conc Mean 0.280000 49.48717 2.309401 4.666667 SourceDFType I ss lab Mean Square F Value Pr>F 18.66666667 9.33333333 1.75 0.2280 Source DFType II sS Mean Square F Value Pr> F lab 18.66666667 9.33333333 1.75 02280