A) Test H0 : σ 2 X = σ 2 Y versus H1 : σ 2 X 6= σ 2 Y with significance level α = 0.05B) Assume σ 2 X = σ 2 Y , construct an one-sided 95% confidence interval with a lower bound for the mean differences in interferon gamma production for drinking tea when compared to coffee, that is, µX − µY . Researchers suspect that drinking tea might enhance the production of interferon gamma, amolecule that helps the immune system fight bacteria, viruses, and tumors. A recent studyinvolved 20 healthy people who did not normally drink tea or coffee. Ten of the participantswere randomly assigned to drink five cups of tea a day, while 10 were asked to drink the sameamount of coffee. After two weeks, blood samples were exposed to an antigen and productionof interferon gamma were measured. The results are shown in the following table:Теа: 55 1754 4910462114553Coffee:1661220 52371522303N(ux,ox) be the interferon gamma production for participants who drink teaand observations for the ten participants who drink tea are a random sample from X. LetN(uy,o?) be the interferon gamma production for participants who drink coffee andobservations for the ten participants who drink coffee are a random sample from Y. Some Routput that may help.> р1 <- с(0.01, 0.025, 0.05, 0.1, о.9, 0.95, 0.975, 0.99)> qnorm(p1)[1] -2.326 -1.960 -1.645 -1.2821.2821.6451.9602.326> qt (p1, 8)[1] -2.896 -2.306 -1.860 -1.3971.397 1.8602.306 2.896> qt(p1, 9)[1] -2.821 -2.262 -1.833 -1.3831.383 1.8332.262 2.821> qt (p1, 18)[1] -2.552 -2.101 -1.734 -1.3301.3301.7342.1012.552> qt(p1, 19)[1] -2.539 -2.093 -1.729 -1.3281.3281.7292.093 2.539> qf (p1, 9, 9)[1] 0.187 O.248 0.315 0.410 2.440 3.179 4.026 5.351> qf (p1, 10, 10)[1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849

The variance between the two samples are tested using the F test. The test statistic of f test is…

Answered: A) Test H0 : σ 2 X = σ 2 Y versus H1 :…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A) Test H0 : σ 2 X = σ 2 Y versus H1 : σ 2 X 6= σ 2 Y with significance level α = 0.05

B) Assume σ 2 X = σ 2 Y , construct an one-sided 95% confidence interval with a lower bound for the mean differences in interferon gamma production for drinking tea when compared to coffee, that is, µX − µY .

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 20 healthy people who did not normally drink tea or coffee. Ten of the participants
were randomly assigned to drink five 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 were measured. The results are shown in the following table:
Теа: 55 17
54 49
10
46
21
14
5
53
Coffee:
16
6
12
20 52
37
15
22
30
3
N(ux,ox) be the interferon gamma production for participants who drink tea
and observations for the ten participants who drink tea are a random sample from X. Let
N(uy,o?) be the interferon gamma production for participants who drink coffee and
observations for the ten participants who drink coffee are a random sample from Y. Some R
output that may help.
> р1 <- с(0.01, 0.025, 0.05, 0.1, о.9, 0.95, 0.975, 0.99)
> qnorm(p1)
[1] -2.326 -1.960 -1.645 -1.282
1.282
1.645
1.960
2.326
> qt (p1, 8)
[1] -2.896 -2.306 -1.860 -1.397
1.397 1.860
2.306 2.896
> qt(p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
1.383 1.833
2.262 2.821
> qt (p1, 18)
[1] -2.552 -2.101 -1.734 -1.330
1.330
1.734
2.101
2.552
> qt(p1, 19)
[1] -2.539 -2.093 -1.729 -1.328
1.328
1.729
2.093 2.539
> qf (p1, 9, 9)
[1] 0.187 O.248 0.315 0.410 2.440 3.179 4.026 5.351
> qf (p1, 10, 10)
[1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849

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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