You'll run a two-sampe t test for independent samples. You sampled 12 treated individuals and 12 different untreated individuals.The fact that the number of animals in each data set is the same does not allow you to conduct a paired t test. There is no special relationship between a data point from one group and any particular data point in the other group. For a two-sample test the numbers in the two groups need not be equal. If one animal dies, you simply compare a set of 11 data points with the set of 12.
This study follows from study #1. Not only did your study suggest that the agent TFK-05W indeed does affect weight gain, but it also proved effective and safe (so far) and it is in clinical trials. Because the drug was designed to treat symptoms that have nothing to do with obesity, the clinical trials do not focus on that problem and won't answer the question of whether or not the agent is a potential weight loss drug. The company, however, has permitted you to test the agent on a group of 12 people with morbid obesity, who have signed the appropriate consent forms.
This time the plan is to treat the 12 obese individuals for a year, having measured their weights on the day treatment was started. The paid participants will be monitoring their weight regularly, taking the drug, and are required to keep a daily log of activity and eating habits so that the experiment can be properly controlled. Nevertheless, the simplest initial test of the hypothesis that obese individuals treated with TFK-05W for a year will show an average weight loss is to compare average weight at the beginning and end of the experiment. Thus, as with study #1, you expect to have two sets of 12 data points each to compare. What statistical test will you use to compare the two means?
Unfortunately, one of your patients died before the year was up. You have 12 data points from the start but can only obtain 11 data points at the end. What do you do?
Reference
TW Kurtz, RC Morris and HA Pershadsingh, The Zucker fatty rat as a genetic
model of obesity and hypertension, Hypertension, Vol 13, 896-901, 1989