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Department
Economics for Management Studies
Course
MGEB12H3
Professor
Vinh Quan
Semester
Summer

Description
Department of Management, UTSC ECMB12 Quantitative Methods in Economics II - Lecture 04 Chapter 9 - Probability of making a type II error Consider testing of mean with population variance known (z-test) eg. Ho: = 0 Ha: 0 = test significance level = P[type I error] = p[reject Ho Ho is true] = P[type II error] = p[fail to reject Ho Ho is false] Power of test = 1- = p[reject Ho Ho is false] Can calculate for any z-tests. How to calculate ? Example 1 Given = 12, sample size n = 36, = 0.05 and hypothesis test H o 120 H a < 120 Reject H of Z 0 - Z If true mean a= 112 and not 120 what is prob. of making a type II error? x x 120 Test StatisticZ 0 0 = n 12 36 Z= Z 0.05 1.645 so -Z =-Z 0.05 -1.645 x 120 Reject H of Z 0 - Z -1.645 or x 116.71 12 36 Therefore fail to reject Ho or commit type II error ifx > 116.71 = P[ x > 116.71] = P[ x 116.71] due to x is continuous RV x E [x ] 116 .71 E [x ] x 116 .71 112 P[ ] = P[ a ] = P[z 2.36] = P[z -2.36] = 0.0091 x x n 12 36 1 www.notesolution.com
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