3. Consider two independent normal distributions N(#1, 400) and N(μ2, 225). Let = μ₁ μ2. Let and denote the observed means of two independent random samples, each of size n, from these two distributions. To test we use the critical region Ho: 0=0, H₁:00, C = {x-> c}. (a) Express the power function K(0) in terms of the standard normal distribution cdf . It depends on n and c. (b) Find n and c so that the probability of type I error is 0.05, and the power at 0 = 10 is 0.9, approximately. Assume that 20.10 = 1.28.
3. Consider two independent normal distributions N(#1, 400) and N(μ2, 225). Let = μ₁ μ2. Let and denote the observed means of two independent random samples, each of size n, from these two distributions. To test we use the critical region Ho: 0=0, H₁:00, C = {x-> c}. (a) Express the power function K(0) in terms of the standard normal distribution cdf . It depends on n and c. (b) Find n and c so that the probability of type I error is 0.05, and the power at 0 = 10 is 0.9, approximately. Assume that 20.10 = 1.28.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 39CR
Related questions
Question
![3. Consider two independent normal distributions N(#1, 400) and N(μ2, 225). Let = μ₁ μ2. Let
and denote the observed means of two independent random samples, each of size n, from these two
distributions. To test
we use the critical region
Ho: 0=0, H₁:00,
C = {x-> c}.
(a) Express the power function K(0) in terms of the standard normal distribution cdf . It depends
on n and c.
(b) Find n and c so that the probability of type I error is 0.05, and the power at 0 = 10 is 0.9,
approximately. Assume that 20.10 = 1.28.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fc235f5-c6fd-4e1c-bac8-7d394d2e8123%2Fe5f50faa-50b8-4234-a148-6f67768bb750%2Fbvycuo_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider two independent normal distributions N(#1, 400) and N(μ2, 225). Let = μ₁ μ2. Let
and denote the observed means of two independent random samples, each of size n, from these two
distributions. To test
we use the critical region
Ho: 0=0, H₁:00,
C = {x-> c}.
(a) Express the power function K(0) in terms of the standard normal distribution cdf . It depends
on n and c.
(b) Find n and c so that the probability of type I error is 0.05, and the power at 0 = 10 is 0.9,
approximately. Assume that 20.10 = 1.28.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 4 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
![Calculus For The Life Sciences](https://www.bartleby.com/isbn_cover_images/9780321964038/9780321964038_smallCoverImage.gif)
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,