Drink Tea for a Stronger Immune System

We have seen that drinking tea appears to offer a strong boost to the immune system. In a study extending the results,1 blood samples were taken on 5 participants before and after one week of drinking about five cups of tea a day (the participants did not drink tea before the study started). The before and after blood samples were exposed to e.coli bacteria, and production of interferon gamma, a molecule that fights bacteria, viruses, and tumors, was measured. Mean production went from 155 pg/mL before tea drinking to 448 pg/mL after tea drinking. The mean difference for the 5 subjects is 293 pg/mL with a standard deviation in the differences of 242. The paper implies that the use of the t-distribution is appropriate.

1 Adapted from Kamath, A., et. al., ‘‘Antigens in tea-beverage prime human Vγ2Vδ2 T cells in vitro and in vivo for memory and non-memory antibacterial cytokine responses," Proceedings of the National Academy of Sciences, May 13, 2003; 100(10): 6009-6014.

(a) Which method is most appropriate for this analysis?
A. Paired data difference in means
B. Difference in means with two separate groups
(b) Find a confidence interval for the mean increase in production of interferon gamma after drinking tea for one week.