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.

Step-by-step explanation:

Hello!

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

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!

sorry i need the points

step-by-step explanation:

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answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.