(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)

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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