Question: Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice.
(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each pair were littermates. A coin toss was used to decide which pig in each pair got Ration A and which got Ration B.
(b) Separate random samples of male and female college professors are taken. We wish to compare the average salaries of male and female teachers.
(c) To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with another fertilizer. A computer's random number generator is used to determine which plots get which fertilizer.