B2. Consider the testing problem where we have observed a random sample ₁,...,n from the model X₁,..., Xn~ N(μ, o²), where the X, are independent, and we want to test the hypothesis Ho: o2 = of against the alternative H₁: 02 o. For the test we use the test statistic y = n Σ i=1 (x₁ - x)² 0² where is the sample mean of the x₁. (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 the probability of a type I error in this case?
B2. Consider the testing problem where we have observed a random sample ₁,...,n from the model X₁,..., Xn~ N(μ, o²), where the X, are independent, and we want to test the hypothesis Ho: o2 = of against the alternative H₁: 02 o. For the test we use the test statistic y = n Σ i=1 (x₁ - x)² 0² where is the sample mean of the x₁. (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 the probability of a type I error in this case?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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