17. The director of human resources for a large bank has compiled data on about
ID: 3356671 • Letter: 1
Question
17. The director of human resources for a large bank has compiled data on about 70 former employees at one of the bank's call centers (see the Excel file Cal Center Data). For each of the following, assume equal variances of the two populations a. Test the null hypothesis that the average length of service for males is the same as for females. b. Test the null hypothesis that the average length of service for individuals without prior call center experience is the same as those with experience Test the nuli hypothesis that the average length of service for individuals with a college degree is the c. same as for individuals without a college degree.Explanation / Answer
a)
Males
Females
3.47
7.02
1.78
2.07
4.42
3.05
3.29
2.95
0.49
2.15
0.61
4.03
3.12
2.15
3.53
1.94
2.47
2.91
3.27
3.02
1.1
2.53
1.78
1.84
2.88
0.98
2.2
2.3
1.44
2.05
2.53
2.13
1.41
1.7
1.08
2.11
0.63
2.15
1.3
1.95
2.13
1.02
2.12
1.26
2.16
1.64
2.04
1.48
1.75
1.31
2.12
1.16
0.37
1.05
1.04
1.24
1.75
0.81
1.71
0.99
1.29
1
1.46
0.57
1.88
1.5
1.16
2
0.96
1
0.87
0.76
0.35
2
0.76
1.787
1.973142857
Mean
0.972934235
1.16451649
SD
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping males as population 1 and females as population 2
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (40-1)*0.97^2+(35-1)*1.1645^2/39+34
= 36.91744+46.1073543/73
= 1.1373
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(1.787-1.973)-0/1.1373(1/40+1/35)
=-0.186/0.2468
=-0.75
tCRIT is +/- 1.99 and hence cannot reject the null hypothesis
b)
No Prior Exp
Prior Exp
7.02
3.47
2.07
4.42
1.78
3.29
3.12
3.05
2.95
0.49
4.03
0.61
3.53
2.15
2.47
2.91
2.15
3.02
3.27
2.53
1.1
2.88
1.78
0.98
1.94
0.63
1.84
2.13
2.2
2.3
1.44
2.05
2.53
2.13
1.41
2.12
1.08
2.12
1.3
1.75
2.16
1.71
2.04
1.48
1.7
1.88
2.11
1.24
1.75
0.87
2.15
0.99
0.37
0.76
1.95
0.35
1.02
0.57
1.26
2
1.04
0.76
1.64
2
1.29
1
1.31
1.46
1.16
1.16
1.05
0.96
0.81
1
1.5
1.902380952
1.837575758
Mean
1.118591906
1.004564677
SD
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping people with No Prior Exp as population 1 and With Prior Exp as population 2
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (42-1)*1.12^2+(33-1)*1.0045^2/41+32
= 51.30+32.29/73
= 1.145
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(1.90-1.8375)-0/1.145(1/42+1/33)
=0.0625/0.2489
=0.25
tCRIT is +/- 1.99 and hence cannot reject the null hypothesis
c)
With college degree
Without college degree
1.78
7.02
0.49
3.47
0.61
2.07
3.12
4.42
2.95
3.29
2.15
3.05
1.1
4.03
1.78
3.53
1.84
2.47
1.44
2.15
1.41
3.27
1.08
1.94
0.98
2.91
0.63
3.02
1.3
2.53
2.13
2.88
2.05
2.2
2.13
2.53
2.12
2.3
2.16
2.04
1.75
1.7
2.15
2.11
0.37
2.12
1.26
1.95
1.64
1.02
1.71
1.04
1.31
1.75
1.16
1.29
1.05
1.48
0.96
1.46
0.81
1.88
0.87
1.16
0.76
1.24
0.35
0.99
0.57
1
2
1.5
0.76
1
2
1.440263158
2.319189189
Mean
0.689980363
1.196927498
SD
H0: 1 - 2 = 0 i.e. (1 = 2)
H1: 1 - 2 0 i.e. (1 2)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping people with college degree as population 1 and Without college degree as population 2
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (38-1)*0.69^2+(37-1)*1.1969^2/37+36
= 17.61+51.57/73
= 0.9478
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(0.4760-1.4326)-0/0.9478(1/38+1/37)
=-0.878926/0.22485206
=-3.91
tCRIT is +/- 1.99 and hence reject the null hypothesis
Males
Females
3.47
7.02
1.78
2.07
4.42
3.05
3.29
2.95
0.49
2.15
0.61
4.03
3.12
2.15
3.53
1.94
2.47
2.91
3.27
3.02
1.1
2.53
1.78
1.84
2.88
0.98
2.2
2.3
1.44
2.05
2.53
2.13
1.41
1.7
1.08
2.11
0.63
2.15
1.3
1.95
2.13
1.02
2.12
1.26
2.16
1.64
2.04
1.48
1.75
1.31
2.12
1.16
0.37
1.05
1.04
1.24
1.75
0.81
1.71
0.99
1.29
1
1.46
0.57
1.88
1.5
1.16
2
0.96
1
0.87
0.76
0.35
2
0.76
1.787
1.973142857
Mean
0.972934235
1.16451649
SD
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