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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.

MATLAB: An Introduction with Applications
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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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.
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.
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