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# Chap11 - Solutions to End-of-Section and Chapter Review...

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Solutions to End-of-Section 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 chi-sq contrib= 0 chi-sq contrib= 0 Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 2 30 30 45 45 75 chi-sq contrib= 0 chi-sq contrib= 0 Total Obs, Col 1 Total Obs, Col 2 GRAND TOTAL 50 75 125 (c) χ 2 = ∑ ( f 0 f e ) 2 f e = 0 + 0 + 0 + 0 = 0. Since 2 χ < 3.841, do not reject H 0 . 11.2 (a) Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 1 20 25 30 25 50 chi-sq contrib= 1.00 chi-sq contrib= 1.00 Observed Freq Expected Freq Observed Freq Expected Freq Total Obs, Row 2 30 25 20 25 50 chi-sq contrib= 1.00 chi-sq contrib= 1.00 Total Obs, Col 1 Total Obs, Col 2 GRAND TOTAL 50 50 100 (b) Decision rule: If 2 χ > 3.841, reject H 0 . Test statistic: χ 2 = ∑ ( f 0 f e ) 2 f e = 1.00 + 1.00 + 1.00 + 1.00 = 4.00 Decision: Since χ 2 calc = 4.00 is above the critical value of 3.841, reject H 0 .

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Chapter 11: Chi-Square 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 Chi-Square Test Statistic 53.8258 p -Value 2.19E-13 Reject the null hypothesis (a) H 0 : p 1 = p 2 H 1 : p 1 p 2 Decision rule: df = 1. If χ 2 > 6.635, reject H 0 . Test statistic: χ 2 = 53.8258 Decision: Since χ 2 calc = 53.8258 is above the upper critical bound of 6.6349, reject H 0 . 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 0 : p 1 = p 2 H 1 : p 1 p 2 where Populations: 1 = males, 2 = females Decision: Since χ 2 calc = 0.0106 is below the upper critical bound of 6.635, do not reject H 0 . 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 χ in (a) and the cal Z in Problem 9.25(a) satisfy the relationship that 2 cal χ 53.8258 = ( 29 2 cal Z = 2 7.34 = - and the p -value obtained in (b) is exactly the same as the p - value in Problem 9.25(b). Similarly, the 2 cal χ in (c) and the cal Z in Problem 9.25(e) satisfy the relationship that 2 cal χ 0.0106 = ( 29 2 cal Z = 2 0.103 = - and the p -value obtained in (c) is exactly the same as the p -value in Problem 9.25(e). 236
Solutions to End-of-Section and Chapter Review Problems 237 11.4 (a) H 0 : p 1 = p 2 H 1 : p 1 p 2 Decision rule: df = 1. If χ 2 > 3.841, reject H 0 .

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