The director of human resources for a large bank has compiled data on about 70 f
ID: 2929161 • Letter: T
Question
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 Call 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.
c. Test the null hypothesis that the average length of service for individuals with a college degree is the same as for individuals without a college degree.
d. Now conduct tests of hypotheses for equality of variances. Were your assumptions of equal variances valid? If not, repeat the test(s) for means using the unequal variance test.
Call Center Data Male = 1Female = 0 Yes = 1
No = 0 Yes = 1
No = 0 Gender Starting Age Prior Call Center Experience College Degree Length of Service (years) 0 18 0 0 7.02 1 18 1 0 3.47 0 19 0 0 2.07 0 19 0 0 1.78 0 19 0 0 4.42 0 19 0 0 3.29 0 19 1 0 3.05 1 19 1 0 0.49 1 19 1 0 0.61 1 19 0 0 3.12 0 20 0 0 2.95 0 20 1 0 2.15 0 20 0 0 4.03 1 20 0 0 3.53 1 20 0 0 2.47 0 21 0 0 2.15 1 21 0 0 3.27 1 21 0 0 1.10 1 21 0 0 1.78 0 22 0 0 1.94 0 22 1 0 2.91 0 23 1 0 3.02 0 23 1 0 2.53 0 23 0 1 1.84 1 23 1 0 2.88 1 23 0 0 2.20 1 23 0 1 1.44 1 24 0 0 2.53 1 24 0 1 1.41 1 24 0 1 1.08 0 25 1 1 0.98 1 25 1 0 0.63 1 25 0 1 1.30 1 25 1 1 2.13 0 26 1 0 2.30 0 26 1 1 2.05 0 26 1 1 2.13 1 26 1 1 2.12 1 26 0 1 2.16 1 27 0 0 2.04 0 28 0 0 1.70 0 28 0 1 2.11 1 29 0 1 1.75 0 30 0 1 2.15 1 30 1 0 2.12 1 30 0 1 0.37 0 31 0 0 1.95 0 31 0 0 1.02 0 31 0 1 1.26 1 31 0 0 1.04 0 32 0 1 1.64 1 32 1 0 1.75 1 32 1 1 1.71 1 33 0 0 1.29 0 34 1 0 1.48 0 34 0 1 1.31 1 34 0 0 1.46 1 34 1 0 1.88 1 36 0 1 1.16 0 39 0 0 1.16 0 39 0 1 1.05 1 39 0 0 0.96 0 40 1 0 1.24 0 40 0 0 0.81 1 41 1 0 0.87 0 43 1 0 0.99 0 43 1 0 0.76 0 45 0 0 0.32 0 47 1 1 0.35 0 50 1 0 0.57
Explanation / Answer
Answer:
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 Call 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.
Two-Sample T-Test and CI: Length of Service, Gender_1
Method
: mean of Length of Service when Gender_1 = 0
µ: mean of Length of Service when Gender_1 = 1
Difference: - µ
Equal variances are assumed for this analysis.
Descriptive Statistics: Length of Service
Gender_1
N
Mean
StDev
SE Mean
0
37
2.01
1.28
0.21
1
33
1.761
0.857
0.15
Estimation for Difference
Difference
Pooled
StDev
95% CI for
Difference
0.252
1.098
(-0.273, 0.776)
Test
Null hypothesis
H: - µ = 0
Alternative hypothesis
H: - µ 0
T-Value
DF
P-Value
0.96
68
0.342
Calculated t=0.96, P=0.342 which is > 0.05 level. Ho is not rejected
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.
Two-Sample T-Test and CI: Length of Service, Prior Call ... r Experience
Method
: mean of Length of Service when Prior Call Center Experience = 0
µ: mean of Length of Service when Prior Call Center Experience = 1
Difference: - µ
Equal variances are assumed for this analysis.
Descriptive Statistics: Length of Service
Prior Call
Center
Experience
N
Mean
StDev
SE Mean
0
43
1.99
1.20
0.18
1
27
1.747
0.907
0.17
Estimation for Difference
Difference
Pooled
StDev
95% CI for
Difference
0.240
1.099
(-0.299, 0.778)
Test
Null hypothesis
H: - µ = 0
Alternative hypothesis
H: - µ 0
T-Value
DF
P-Value
0.89
68
0.378
Calculated t=0.89, P=0.378 which is > 0.05 level. Ho is not rejected.
The average length of service for individuals without prior call center experience is the same as those with experience.
c. Test the null hypothesis that the average length of service for individuals with a college degree is the same as for individuals without a college degree.
Two-Sample T-Test and CI: Length of Service, College Degree
Method
: mean of Length of Service when College Degree = 0
µ: mean of Length of Service when College Degree = 1
Difference: - µ
Equal variances are assumed for this analysis.
Descriptive Statistics: Length of Service
College
Degree
N
Mean
StDev
SE Mean
0
48
2.06
1.24
0.18
1
22
1.523
0.554
0.12
Estimation for Difference
Difference
Pooled
StDev
95% CI for
Difference
0.542
1.076
(-0.011, 1.095)
Test
Null hypothesis
H: - µ = 0
Alternative hypothesis
H: - µ 0
T-Value
DF
P-Value
1.96
68
0.055
Calculated t=1.96, P=0.055 which is > 0.05 level. Ho is not rejected.
The average length of service for individuals with a college degree is the same as for individuals without a college degree.
d. Now conduct tests of hypotheses for equality of variances. Were your assumptions of equal variances valid? If not, repeat the test(s) for means using the unequal variance test.
Test and CI for Two Variances: Length of Service vs Gender_1
Method
: standard deviation of Length of Service when Gender_1 = 0
: standard deviation of Length of Service when Gender_1 = 1
Ratio: /
The Bonett and Levene's methods are valid for any continuous distribution.
Descriptive Statistics
Gender_1
N
StDev
Variance
95% CI for
0
37
1.275
1.626
(0.810, 2.118)
1
33
0.857
0.734
(0.697, 1.119)
Ratio of Standard Deviations
Estimated
Ratio
95% CI for
Ratio using
Bonett
95% CI for
Ratio using
Levene
1.48840
(0.675, 2.284)
(0.760, 1.932)
Test
Null hypothesis
H: / = 1
Alternative hypothesis
H: / 1
Significance level
= 0.05
Method
Test
Statistic
DF1
DF2
P-Value
Bonett
*
0.246
Levene
1.01
1
68
0.318
Calculated P=0.318 which is > 0.05 level. Ho is not rejected.
The assumptions of equal variances is valid.
Test and CI for Two Variances: Length of Service vs Prior ... Experience
Method
: standard deviation of Length of Service when Prior Call Center Experience = 0
: standard deviation of Length of Service when Prior Call Center Experience = 1
Ratio: /
The Bonett and Levene's methods are valid for any continuous distribution.
Descriptive Statistics
Prior Call
Center
Experience
N
StDev
Variance
95% CI for
0
43
1.203
1.447
(0.773, 1.962)
1
27
0.907
0.822
(0.764, 1.161)
Ratio of Standard Deviations
Estimated
Ratio
95% CI for
Ratio using
Bonett
95% CI for
Ratio using
Levene
1.32674
(0.566, 2.052)
(0.578, 1.623)
Test
Null hypothesis
H: / = 1
Alternative hypothesis
H: / 1
Significance level
= 0.05
Method
Test
Statistic
DF1
DF2
P-Value
Bonett
*
0.431
Levene
0.05
1
68
0.823
Calculated P=0.823 which is > 0.05 level. Ho is not rejected.
The assumptions of equal variances is valid.
Test and CI for Two Variances: Length of Service vs College Degree
Method
: standard deviation of Length of Service when College Degree = 0
: standard deviation of Length of Service when College Degree = 1
Ratio: /
The Bonett and Levene's methods are valid for any continuous distribution.
Descriptive Statistics
College
Degree
N
StDev
Variance
95% CI for
0
48
1.240
1.537
(0.875, 1.832)
1
22
0.554
0.307
(0.417, 0.810)
Ratio of Standard Deviations
Estimated
Ratio
95% CI for
Ratio using
Bonett
95% CI for
Ratio using
Levene
2.23679
(1.067, 3.637)
(1.184, 2.943)
Test
Null hypothesis
H: / = 1
Alternative hypothesis
H: / 1
Significance level
= 0.05
Method
Test
Statistic
DF1
DF2
P-Value
Bonett
*
0.035
Levene
6.12
1
68
0.016
Calculated P=0.016 which is < 0.05 level. Ho is rejected.
The assumptions of equal variances is not valid.
Two-Sample T-Test and CI: Length of Service, College Degree
Method
: mean of Length of Service when College Degree = 0
µ: mean of Length of Service when College Degree = 1
Difference: - µ
Equal variances are not assumed for this analysis.
Descriptive Statistics: Length of Service
College
Degree
N
Mean
StDev
SE Mean
0
48
2.06
1.24
0.18
1
22
1.523
0.554
0.12
Estimation for Difference
Difference
95% CI for
Difference
0.542
(0.114, 0.970)
Test
Null hypothesis
H: - µ = 0
Alternative hypothesis
H: - µ 0
T-Value
DF
P-Value
2.53
67
0.014
Calculated t=2.53, P=0.014 which is <0.05 level. Ho is not rejected.
The average length of service for individuals with a college degree is not same as for individuals without a college degree.
: mean of Length of Service when Gender_1 = 0
µ: mean of Length of Service when Gender_1 = 1
Difference: - µ