You are sampling from two different populations, so if you do a t test it must be a two-sample test.
For all case studies, assume that the investigator has used appropriate tests to find that the data are normally distributed and meet the criteria for equal variances.
As a biochemist working for a pharmaceutical company, your job is to test new drugs for possible side effects, both deterimental and beneficial. The chemistry of agent TFK-05W suggests that it may have the side effect of reducing the tendency toward obesity. The Zucker rat is an established genetic model for both obesity and hypertension. As rats of the obese strain age they gain weight much more rapidly than do the so-called "lean" Zucker strain. You plan to treat a group of Zucker rats over a period of one year and compare their average weight with that of a group of untreated animals.
The odds of the drug actually showing this side effect are small and maintenance of rats for a year is expensive, so you limited the scope of the study to twelve animals in each group. The null hypothesis is that treated animals will show an average weight gain over one year that is no different from the average weight gain of untreated animals. What statistical test will you use to compare the two means?
One of the Zucker rats died before the year was up. Does this turn of events ruin your experiment?
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