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Unformatted text preview: Solutions to EndofSection and Chapter Review Problems 235 CHAPTER 11 11.1 (a)(b) Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 1 20 20 30 30 50 chisq contrib= 0 chisq contrib= 0 Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 2 30 30 45 45 75 chisq contrib= 0 chisq contrib= 0 Total Obs, Col 1 Total Obs, Col 2 GRAND TOTAL 50 75 125 (c) 2 = ( f f e ) 2 f e = 0 + 0 + 0 + 0 = 0. Since 2 < 3.841, do not reject H . 11.2 (a) Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 1 20 25 30 25 50 chisq contrib= 1.00 chisq contrib= 1.00 Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 2 30 25 20 25 50 chisq contrib= 1.00 chisq contrib= 1.00 Total Obs, Col 1 Total Obs, Col 2 GRAND TOTAL 50 50 100 (b) Decision rule: If 2 > 3.841, reject H . Test statistic: 2 = ( f f e ) 2 f e = 1.00 + 1.00 + 1.00 + 1.00 = 4.00 Decision: Since 2 calc = 4.00 is above the critical value of 3.841, reject H . Chapter 11: ChiSquare and Nonparametric Tests 11.3 (a) Excel output: Observed Frequencies Gender Enjoy Shopping Male Female Total Yes 136 224 360 No 104 36 140 Total 240 260 500 Expected Frequencies Gender Enjoy Shopping Male Female Total Yes 172.8 187.2 360 No 67.2 72.8 140 Total 240 260 500 Level of Significance 0.01 Number of Rows 2 Number of Columns 2 Degrees of Freedom 1 Results Critical Value 6.634891 ChiSquare Test Statistic 53.8258 pValue 2.19E13 Reject the null hypothesis (a) H : p 1 = p 2 H 1 : p 1 p 2 Decision rule: df = 1. If 2 > 6.635, reject H . Test statistic: 2 = 53.8258 Decision: Since 2 calc = 53.8258 is above the upper critical bound of 6.6349, reject H . There is enough evidence to conclude that there is a significant difference between the proportions of males and females who enjoy shopping for clothing at the 0.01 level of significance. (b) p value = virtually zero. The probability of obtaining a test statistic as large as 53.8258 or larger when the null hypothesis is true is virtually zero. (c) (a) H : p 1 = p 2 H 1 : p 1 p 2 where Populations: 1 = males, 2 = females Decision: Since 2 calc = 0.0106 is below the upper critical bound of 6.635, do not reject H . There is not enough evidence to conclude that the proportion of males and females who enjoy shopping for clothing are different. (b) p value = 0.9180. The probability of obtaining a test statistic larger than 0.0106 or more when the null hypothesis is true is 0.9180. (d) The results of (a) (c) are exactly the same as those of Problem 9.25. The 2 cal in (a) and the cal Z in Problem 9.25(a) satisfy the relationship that 2 cal 53.8258 = ( 29 2 cal Z = 2 7.34 =  and the pvalue obtained in (b) is exactly the same as the p value in Problem 9.25(b). Similarly, the 2 cal in (c) and the cal Z in Problem 9.25(e) satisfy the relationship that 2 cal 0.0106 = ( 29 2 cal Z = 2 0.103 =  and the pvalue obtained in (c) is exactly the same as the...
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Harris

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