We have seen that drinking tea appears to offer a strong boost to the immune system. In a study extending the results,1 blood sample was 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 the 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.
(a) Use the information to test whether the mean production of interferon-gamma as a response to bacteria is significantly higher after drinking tea than before drinking tea. Use a 5 % significance level.
(b) Give the test statistic and the p-value
Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.
(c) Is there evidence that the mean production of interferon-gamma is higher after drinking tea?