Archaeologists can determine the diets of ancient civilizations by measuring the ratio of carbon-13 to carbon-12 in bones found at burial sites. Large amounts of carbon-13 suggest a diet rich in grasses such as maize, while small amounts suggest a diet based on herbaceous plants. The article ??Climate and Diet in Fremont Prehistory: Economic Variability and Abandonment of Maize Agriculture in the Great Salt Lake Basin?? (J. Coltrain and S. Leavitt, American Antiquity, 2002:453??485) reports ratios, as a difference from a standard in units of parts per thousand, for bones from individuals in several age groups. The data are presented in the following table.

a. Construct an ANOVA table. You may give a range for the P-value.

b. Can you conclude that the concentration ratios differ among the age groups?

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Age Group (years) Ratio 0-11 17.2 18.4 17.9 16.6 19.0 18.3 13.6 13.5 18.5 19.1 19.1 13.4 12–24 14.8 17.6 18.3 17.2 10.0 11.3 10.2 17.0 18.9 19.2 25-45 18.4 13.0 14.8 18.4 12.8 17.6 18.8 17.9 18.5 17.5 18.3 15.2 10.8 19.8 17.3 19.2 15.4 13.2 46+ 15.5 18.2 12.7 15.1 18.2 18.0 14.4 10.2 16.7