21-25 The Excel file Accounting Professionals provides the results of a survey o

Question

21-25

The Excel file Accounting Professionals provides the results of a survey of 27 employees in a tax division of a Fortune100 company. Test the null hypothesis that the average number of years of service is the same for males and females

(Significance level 5%)

Accounting Department Survey Data Employee Gender Years of Service Years Undergraduate Study Graduate Degree? CPA? Age Group 1 F 17 4 N Y 41-45 2 F 6 2 N N 26-30 3 M 8 4 Y Y 31-35 4 F 8 4 Y N 31-35 5 M 16 4 Y Y 36-40 6 F 21 1 N Y 51-55 7 M 27 4 N N 51-55 8 F 7 4 Y Y 26-30 9 M 8 4 N N 31-35 10 M 23 2 N Y 41-45 11 F 9 4 Y Y 31-35 12 F 8 2 N N 26-30 13 F 8 4 Y N 26-30 14 M 26 4 N Y 46-50 15 F 9 4 N Y 26-30 16 F 9 2 N N 26-30 17 M 19 2 Y Y 36-40 18 M 5 4 N N 36-40 19 M 19 4 Y N 51-55 20 M 20 4 N N 46-50 21 F 14 4 Y Y 36-40 22 M 31 4 N N 51-55 23 F 10 0 N N 51-55 24 F 10 4 N Y 31-35 25 M 26 4 Y Y 46-50 26 M 28 4 N N 51-55 27 F 5 4 N Y

21-25

Explanation / Answer

Years of Service. Years Undergraduate Study Employee Gender Years of Service. Years Undergraduate Study CPA? Graduate Degree? Age Group Female Male Female Male 1 F 17 4 Y N 5 The Excel file Accounting Professionals.xls provides the results of a survey of 27 employees in a tax 17 8 4 4 2 F 6 2 N N 2 division of a Fortune 100 company. 6 16 2 4 4 F 8 4 N Y 3 a. Test the hypothesis that the average number of years of service is the same for males and 8 27 4 4 6 F 21 1 Y N 7 females. 21 8 1 4 8 F 7 4 Y Y 2 7 23 4 2 11 F 9 4 Y Y 3 9 26 4 4 12 F 8 2 N N 2 8 19 2 2 13 F 8 4 N Y 2 8 5 4 4 15 F 9 4 Y N 2 9 19 4 4 16 F 9 2 N N 2 Note: assume alpha = .05 9 20 2 4 21 F 14 4 Y Y 4 14 31 4 4 23 F 10 0 N N 7 a. Two Sample Tests for Means, Standard Deviation Unknown, Assumed Unequal: 10 26 0 4 24 F 10 4 Y N 3 CASE 3 10 28 4 4 27 F 5 4 Y N 1 H0: The average number of years of service is the same for males and females. 5 4 3 M 8 4 Y Y 3 H1: The average number of years of service is not the same for males and females. 5 M 16 4 Y Y 4 9 M 8 4 N N 3 Female Male 14 13 10 M 23 2 Y N 5 n 14 13 3.071429 3.692308 14 M 26 4 Y N 6 mean 10.0714 19.6923 1.917582 0.564103 17 M 19 2 Y Y 4 variance 19.3022 70.3974 18 M 5 4 N N 4 alpha 0.05 19 M 19 4 N Y 7 df 17 (rounded down) 20 M 20 4 N N 6 t critical 2.1098 22 M 31 4 N N 7 t -3.6911 =INT((D22/D20+E22/E20)^2/(((D22/D20)^2/(D20-1))+((E22/E20)^2/(E20-1)))) 25 M 26 4 Y Y 6 26 M 28 4 N N 7 Reject H0 (two tail test). Age Group Age Range 1 21-25 t = (`x1 - `x2 ) / 2 26-30 3 31-35 4 36-40 5 41-45 df* = 6 46-50 7 51-55 F CI for variances 8 56-60 Female Male 9 over 60 n 14 13 mean 10.0714 19.6923 b. Two Sample Tests for Means, Standard Deviation Unknown, Assumed Unequal: variance 19.3022 70.3974 H0: The average years of undergraduate study is the same for males and females. F-large 3.239263 H1: The average years of undergraduate study is not the same for males and females. F-small 0.317141 Female Male CI-lower 0.084645 n 14 13 CI-upper 0.864566 mean 3.0714 3.6923 variance 1.9176 0.5641 Note that 1 is not in the F-CI. Therefore, we should use Case 3 for the means interval. alpha 0.05 df 20 (rounded down) F test for variances t critical 2.0860 Ho: var1/var2 = 1 t -1.4620 Ha: var1/var2 < 1 alpha = .05 Cannot reject H0 (two tail test). F = (samplevar1/samplevar2)/(1) c. Chi-square Test: F-crit = 0.317141 =FINV(0.975,K39-1,L39-1) H0: age group is independent of having a graduate degree. F* = 0.274189 H1: age group is not independent of having a graduate degree. F* is in the CR; therefore, reject Ho. Observed Frequencies: Graduate Degree? Age Group N Y Grand Total 1 1 0 1 2 4 2 6 3 2 3 5 4 1 3 4 5 2 0 2 6 2 1 3 7 4 1 5 Grand Total 16 10 26 Expected Frequencies: Graduate Degree? Age Group N Y Grand Total 1 0.615384615 0.384615385 1 2 3.692307692 2.307692308 6 3 3.076923077 1.923076923 5 4 2.461538462 1.538461538 4 5 1.230769231 0.769230769 2 6 1.846153846 1.153846154 3 7 3.076923077 1.923076923 5 Grand Total 16 10 26 df 6 alpha 0.05 c2 critical 12.5916 p-value 0.4309 c2 5.9313 Cannot reject H0

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