For the data described below select the proper statistical t

For the data described below, select the proper statistical test/tests to compare the means of each set of sample data as described below. If not, identify which two sets of sample data have significant differences between their respective means for each a value. (Sample One versus Sample Two at a values = to 0.05,0.10 and 0.15, Sample Two versus Sample Three at a values = to 0.05,0.10 and 0.15, etc.) Justify your conclusions by comparing the probability of them being significantly different with the value of the test statistic that you chose to utilize. Organize your results in a table. 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 amount 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 of 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.

Solution

Total sum of squares= 13272.38-12898.4694=373.9106. SST=(3488.43+2387.025+4897.2001+2146.7778)-12898.4694=20.9635, SSE=373.9106-20.9634=352.9471. F=(20.9635/3)/(352.9471/45)=6.9878/7.8433=0.8909. The table value of F (3,60) at .05 & 0.1 is 2.7581 & 2.18. Here Fcal<Ftab so we accept null hypothesis. Therefore, there is no significant difference between the means of the samples at 0.05 & 0.10.