We saw in Exercise 6.260 on page 425 that drinking tea appears to offer a strong boost to the immune system. In a study extending the results of the study described in that exercise, blood samples were taken on five 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 five 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.

(a) Why is it appropriate to use paired data in this analysis?

(b) Find and interpret a 90% confidence interval for the mean increase in production of interferon gamma after drinking tea for one week.

Exercise 6.260 on page 425

Drinking tea appears to offer a strong boost to the immune system. In a study introduced in Exercise 3.82 on page 203, we see that production of interferon gamma, a molecule that fights bacteria, viruses, and tumors, appears to be enhanced in tea drinkers. In the study, eleven healthy non-tea-drinking individuals were asked to drink five or six cups of tea a day, while ten healthy nontea- and non-coffee-drinkers were asked to drink the same amount of coffee, which has caffeine but not the L-theanine that is in tea. The groups were randomly assigned. After two weeks, blood samples were exposed to an antigen and production of interferon gamma was measured. The results are shown in Table 6.23 and are available in ImmuneTea. The question of interest is whether the data provide evidence that production is enhanced in tea drinkers.

Table 6.23

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20 Tea 11 47 5 13 55 18 48 52 56 58 11 Coffee 3 15 16 21 21 38 52