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(iii) Now, suppose we want to test H₁ : µx = µy against H₁ : µx > µy at significance level 0.05, by drawing a sample of size n from the distribution of X and a sample of size m from the distribution of Y. Let d = x - y. For d > 0, compute the power K(d) of the test as a function of d. (Your answer will involve n, m, and the standard normal distribution.) (iv) What is the minimum combined sample size n + m needed in order to ensure K(d) ≥ 0.95 for d> 1?

(iii) Now, suppose we want to test H₁ : µx = µy against H₁ : µx > µy at significance level 0.05, by drawing a sample of size n from the distribution of X and a sample of size m from the distribution of Y. Let d = x - y. For d > 0, compute the power K(d) of the test as a function of d. (Your answer will involve n, m, and the standard normal distribution.) (iv) What is the minimum combined sample size n + m needed in order to ensure K(d) ≥ 0.95 for d> 1?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please show me the answer of question 3 and 4

(iii) Now, suppose we want to test H₁ : µx = µy against H₁ : µx > µy at significance level 0.05, by drawing a sample of size n from the distribution of X and a sample of size m from the distribution of Y. Let d = x - y. For d > 0, compute the power K(d) of μχ the test as a function of d. (Your answer will involve n, m, and the standard normal distribution.) (iv) What is the minimum combined sample size n + m needed in order to ensure K(d) > 0.95 for d> 1?
Transcribed Image Text:(iii) Now, suppose we want to test H₁ : µx = µy against H₁ : µx > µy at significance level 0.05, by drawing a sample of size n from the distribution of X and a sample of size m from the distribution of Y. Let d = x - y. For d > 0, compute the power K(d) of μχ the test as a function of d. (Your answer will involve n, m, and the standard normal distribution.) (iv) What is the minimum combined sample size n + m needed in order to ensure K(d) > 0.95 for d> 1?
Let X ~ N(μx, 16) and Y ~ N(µy, 36). = (i) Suppose we want to test Ho x = 7 against H₁ μx : : µx 8 at significance level a = 0.05, by drawing a sample of size n from the distribution of X. What is the type II error probability 3? (Your answer will involve n and the standard normal distribution.) (ii) What is the minimum sample size n needed in order to ensure ß ≤ 0.05?
Transcribed Image Text:Let X ~ N(μx, 16) and Y ~ N(µy, 36). = (i) Suppose we want to test Ho x = 7 against H₁ μx : : µx 8 at significance level a = 0.05, by drawing a sample of size n from the distribution of X. What is the type II error probability 3? (Your answer will involve n and the standard normal distribution.) (ii) What is the minimum sample size n needed in order to ensure ß ≤ 0.05?
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