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 a Climate and Diet in Fremont Prehistory: Economic Variability and Abandonment of Maize Agriculture in the Great Salt Lake Basina (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. 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
(a) Construct a complete ANOVA table.
(b) Can you conclude that the concentration ratios differ among the age groups?
(c) Does this data set meet the conditions of the global F test? You need to prove why or why not using plots and other analysis.
(d) UseFisher’sLSDtoconstructconfidenceintervalsforallpair-wisecomparison’softhegroups.
(e) Use Bonferroni’s method to construct confidence intervals for all pair-wise comparison’s of the groups. You may use RStudio to get the appropriate critical value.
(f) Use the Tukey-Kramer method to construct confidence intervals for all pair-wise comparison’s of the groups.
Let x represent the amount of money you originally had. The algebraic expression would be: x-20+3×=80. If you want to solve the equation, it would be: 4x=100, and x=100÷4, which equals 25. So your original money was $25.
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: ( 8 , − 3 ) Equation Form: x = 8 , y = − 3
