Consider two independent normal distributions N(#1, 400) and N(#2, 225). Let 0 μ₁₂. Let T and y 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, H1:0>0, C={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 = 10 is 0.9, approximately. Assume that zo.10 = 1.28.
Consider two independent normal distributions N(#1, 400) and N(#2, 225). Let 0 μ₁₂. Let T and y 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, H1:0>0, C={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 = 10 is 0.9, approximately. Assume that zo.10 = 1.28.
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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Transcribed Image Text:Consider two independent normal distributions N(#1, 400) and N(#2, 225). Let 0 μ₁₂. Let T
and y 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, H1:0>0,
C={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 = 10 is 0.9,
approximately. Assume that zo.10 = 1.28.
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