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 53 Coffee: 16 12 20 52 37 15 22 30 3 Let X ~ N(ux,o3) 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 Y ~ 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. > p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 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 > qt (p1, 9) [1] -2.821 -2.262 -1.833 -1.383 > qt (p1, 18) 1.397 1.860 2.306 2.896 1.383 1.833 2.262 2.821 [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 > qf (p1, 9, 9) [1] 0.187 0.248 0.315 0.410 2.440 3.179 4.026 5.351 > qf (p1, 10, 10) 1.328 1.729 2.093 2.539 [1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849 (a) Let X* be a future observation of X, find a two-sided 95% prediction interval for X*.
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 53 Coffee: 16 12 20 52 37 15 22 30 3 Let X ~ N(ux,o3) 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 Y ~ 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. > p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 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 > qt (p1, 9) [1] -2.821 -2.262 -1.833 -1.383 > qt (p1, 18) 1.397 1.860 2.306 2.896 1.383 1.833 2.262 2.821 [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 > qf (p1, 9, 9) [1] 0.187 0.248 0.315 0.410 2.440 3.179 4.026 5.351 > qf (p1, 10, 10) 1.328 1.729 2.093 2.539 [1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849 (a) Let X* be a future observation of X, find a two-sided 95% prediction interval for X*.
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
Related questions
Question
![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
53
Coffee: 16
12 20 52 37 15 22 30
3
Let X ~
N(ux,o3) 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
Y ~ 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.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 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
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
> qt (p1, 18)
1.397
1.860 2.306 2.896
1.383
1.833 2.262 2.821
[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
> qf (p1, 9, 9)
[1] 0.187 0.248 0.315 0.410 2.440 3.179 4.026 5.351
> qf (p1, 10, 10)
1.328
1.729 2.093
2.539
[1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849
(a) Let X* be a future observation of X, find a two-sided 95% prediction interval for X*.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F433c14e3-652f-4add-95c2-5fe04b0fff82%2Fe87aafc6-17aa-4e7d-9180-4cb882574931%2Fbi6439_processed.png&w=3840&q=75)
Transcribed Image Text: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
53
Coffee: 16
12 20 52 37 15 22 30
3
Let X ~
N(ux,o3) 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
Y ~ 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.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 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
> qt (p1, 9)
[1] -2.821 -2.262 -1.833 -1.383
> qt (p1, 18)
1.397
1.860 2.306 2.896
1.383
1.833 2.262 2.821
[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
> qf (p1, 9, 9)
[1] 0.187 0.248 0.315 0.410 2.440 3.179 4.026 5.351
> qf (p1, 10, 10)
1.328
1.729 2.093
2.539
[1] 0.206 0.269 0.336 0.431 2.323 2.978 3.717 4.849
(a) Let X* be a future observation of X, find a two-sided 95% prediction interval for X*.
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