Chapter 10 Problem4

# Chapter 10 Problem4 - Critical value...

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QAS129:001 Instructor: Dr. Yudan Zheng 1. A sample of 500 shoppers was selected in a large metropolitan area to determine various information concerning consumer behavior. Among the questions asked was, “Do you enjoy shopping for clothing?” Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. Is there evidence of a significant difference between males and females in the proportion who enjoy shopping for clothing at the 0.01 level of significance? ANSWER: 1 2 1 2 1 2 136 224 0.567, 0.862, 240 260 X X p p n n = = = = = = and p = X 1 + X 2 n 1 + n 2 = 136 + 224 240 + 260 = 0.72 P1=x1/n1=0.567 p2=x2/n2=0/862 /p=(x1+x2)/(n1+n2)= (136+224)/(240+260)=0.72 Hypotheses are: H 0 : 1 π = 2 H 1 : 1 2 where Populations: 1 = males, 2 = females
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Unformatted text preview: Critical value 1=normsinv(0.01/2)==-2.58, critical value 2=2.58 Therefore, decision rule: If Z < – 2.58 or Z > 2.58, reject H . Test statistic: ( 29 ( 29 ( 29 ( 29 + ×-= +----= 260 1 240 1 28 . 72 . 0.862-0.567 1 1 1 2 1 2 1 2 1 n n p p p p Z =-7.34 Z=(p1-p2)-(pi1-pi2)/ /p(1-/p)(1/n1 +1/n2) Decision: Since Z = – 7.34 is well below the lower critical bound of – 2.58, reject H . There is sufficient evidence to conclude that a significant difference exists in the proportion of males and females who enjoy shopping for clothing....
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## This note was uploaded on 12/10/2010 for the course STAT QAS 129 taught by Professor Zheng during the Fall '10 term at Long Island U..

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