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

(a) Is this an experiment or an observational study?

(b) What are the null and alternative hypotheses?

(c) Find a standardized test statistic and use the t-distribution to find the p-value and make a conclusion.

(d) Always plot your data! Look at a graph of the data. Does it appear to satisfy a normality condition?

(e) A randomization test might be a more appropriate test to use in this case. Construct a randomization distribution for this test and use it to find a p-value and make a conclusion.

(f) What conclusion can we draw?

Exercise 3.82

Researchers suspect that drinking tea might enhance the production of interferon gamma, a molecule that helps the immune system fight bacteria, viruses, and tumors. A recent study involved 21 healthy people who did not normally drink tea or coffee. Eleven of the participants were randomly assigned to drink five or six cups of tea a day, while 10 were asked to drink the same amount of coffee. After two weeks, blood samples were exposed to an antigen and production of interferon gamma was measured. The results are shown in Table 3.12 and are available in ImmuneTea. We are interested in estimating the effect size, the increase in average interferon gamma production for drinking tea when compared to coffee. Use StatKey or other technology to estimate the difference in mean production for tea drinkers minus coffee drinkers. Give the standard error for the difference and a 95% confidence interval. Interpret the result in context.

Table 3.12

Transcribed Image Text:

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