In an investigation of the possible influence of di- etary 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.3 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 three and two.

(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?