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 5% significance level. 1Adapted 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. Give the test statistic and the p-value. 1) Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = p-value = 2) Give the conclusion using a 5% significance level. a) Reject H0. b) Do not reject H0. 3) Is there evidence that mean production of interferon gamma is higher after drinking tea? a) Yes b) No

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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 5% significance level.

¹Adapted 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.

Give the test statistic and the p-value.

1) Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

test statistic =

p-value =

2) Give the conclusion using a 5% significance level.

a) Reject H0.

b) Do not reject H0.

3) Is there evidence that mean production of interferon gamma is higher after drinking tea?

a) Yes

b) No

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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