Testing the Effects of Tea on the 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. Use the information to test whether mean production of interferon gamma as a response to bacteria is significantly higher after drinking tea than before drinking tea. Use a significance level.

To test the effects of Tea on the immune system, a sample of 5 participants was taken and their production of interferon-γ in presence of E.coli before drinking Tea and after drinking tea for a week was measured.

This is an example of a paired sample test, the variable of interest is:

Xd: Difference between the production of interferon-γ before drinking Tea and after drinking tea for a week of an individual.

X[bar]before= 155 pg/ml - and X[bar]after= 448pg/ml= X[bar]d= 293 pg/ml

Sd= 242 pg/ml

n= 5 individuals

Assuming that the variable Xd has a normal distribution, you need to test is the population mean of interferon-γ production increases when the individual drinks Tea, symbolically: μd < 0

(If the variable is determined as "before-after" then is logical that the population mean will be negative if the "after" results are greater than the "before" results)

The hypotheses are:

H₀: μd ≥ 0

H₁: μd < 0

α: 0.05

[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]

[tex]t_{H_0}= \frac{293-0}{\frac{242}{\sqrt{5} } } = 2.707= 2.71[/tex]

The p-value of the test is 0.026769

The p-value is less than the significance level, the decision is to reject the null hypothesis.

Then using a significance level of 5%, there is enough evidence to conclude that the population mean of the difference in the production of interferon-γin presence of E.coli before and after drinking Tea fro a week is less than zero. This means that drinking Tea increases the average production of interferon-γ.

I hope this helps!