In an investigation of the possible influence of dietary chromium on diabetic symptoms, some rats were fed a low-chromium diet, and others were fed a normal diet. One response variable was activity of the liver enzyme GITH, which was measured using a radioactively labeled molecule. The accompanying table shows the results, expressed as thousands of counts per minute per gram of liver. The sample means are 49.17 for the low-chromium diet and 51.90 for the normal diet; thus the difference in sample means is -2.73. There are 10 possible randomizations of the five observations into two groups, of sizes 3 and 2.
(a) Create a list of these 10 randomizations (one of which is the original assignment of observations to the two groups) and for each case calculate the low-chromium diet mean minus the normal diet mean.
(b) How many of the 10 randomizations yield a difference in sample means as far from zero as -2.73, the difference in sample means for our observed samples?
(c) Is there evidence that dietary chromium affects GITH liver enzyme activity? Justify your answer using the randomization results.

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Low-chromium diet 42.3 51.5 53.7 Normal diet 53.1 50.7