B2. Consider the testing problem where we have observed a random sample x₁,...,n fromthe model X₁,..., Xn ~ N(µ, o²), where the X, are independent, and we want to testthe hypothesis Ho: o² = o against the alternative H₁: 0² o. For the test we usethe test statisticny = Σi=1(x₁ - x)²0²where is the sample mean of the ₁.(a) What are the type I errors and type II errors in this testing problem?(b) If Ho is true, what is the distribution of the random variable Y corresponding to y?(c) Assume that n = 20 and we reject Ho if and only if y> 32.852. What is theprobability of a type I error in this case?(d)now that H₁ is true for the test in part (c). Draw a sketch of the type IIerror as a function of o2. (There is no need to calculate explicit values.)-(e) Explain why the test described in part (c) is not a good test for testing the hypoth-esis Ho: 0² o against the alternative H₁: o² o2. How would you improvethe test?

As per our guidelines, we are supposed to answer only 3 sub-parts.In this problem we are performing…

Answered: B2. Consider the testing problem where…

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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