Expert answer:Statistics problem set homework help
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Week 4
Confidence Intervals and Chi Square (Chs 11 – 12)
For questions 3 and 4 below, be sure to list the null and alternate hypothesis statements. Use .05 for your si
For full credit, you need to also show the statistical outcomes – either the Excel test result or the calculation
Using our sample data, construct a 95% confidence interval for the population’s me
Interpret the results. How do they compare with the findings in the week 2 one sam
Mean St error t value
Low
to
Males
Females
2
Using our sample data, construct a 95% confidence interval for the mean salary diff
How does this compare to the findings in week 2, question 2?
Difference St Err. T value
Low
to
Yes/No
Can the means be equal?
Why?
How does this compare to the week 2, question 2 result (2 sampe t-test)?
a. Why is using a two sample tool (t-test, confidence interval) a better choice than usin
<1 point>
3
We found last week that the degree values within the population do not impact com
This does not mean that degrees are distributed evenly across the grades and gende
Do males and females have athe same distribution of degrees by grade?
(Note: while technically the sample size might not be large enough to perform this t
What are the hypothesis statements:
Ho:
Ha:
Note: You can either use the Excel Chi-related functions or do the calculations manually.
Data input tables – graduate degrees by gender and grade level
A
B
C
D
E
F
Total
OBSERVED
M Grad
Fem Grad
Male Und
Female Und
EXPECTED
M Grad
Fem Grad
Male Und
Female Und
Interpretation:
What is the value of the chi square statistic:
What is the p-value associated with this value:
Is the p-value <0.05?
Do you reject or not reject the null hypothesis:
If you rejected the null, what is the Cramer's V correlation:
What does this correlation mean?
What does this decision mean for our equal pay question:
<1 point>
4
Based on our sample data, can we conclude that males and females are distributed a
within the population?
What are the hypothesis statements:
Ho:
Ha:
A
B
C
OBS COUNT – m
OBS COUNT – f
EXPECTED
What is the value of the chi square statistic:
What is the p-value associated with this value:
Is the p-value <0.05?
Do you reject or not reject the null hypothesis:
If you rejected the null, what is the Phi correlation:
What does this correlation mean?
D
E
F
What does this decision mean for our equal pay question:
<2 points> 5.
How do you interpret these results in light of our question about equal pay for equal work?
ents. Use .05 for your significance level in making your decisions.
result or the calculations you performed.
for the population’s mean salary for each gender.
gs in the week 2 one sample t-test outcomes (Question 1)?
High
divided by the square root of the sample size.>
for the mean salary difference between the genders in the population.
High
ampe t-test)?
a better choice than using 2 one-sample techniques when comparing two samples?
ation do not impact compa rates.
ss the grades and genders.
es by grade?
enough to perform this test, ignore this limitation for this exercise.)
If desired, you can do manual calculations per cell here.
A
B
C
D
E
F
M Grad
Fem Grad
Male Und
Female Und
Sum =
For this exercise – ignore the requirement for a correction factor
for cells with expected values less than 5.
females are distributed across grades in a similar pattern
Do manual calculations per cell here (if desired)
A
B
C
D
E
M
F
Sum =
F
equal work?
ID
Salary
Compa
Midpoint
Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
64.4
27.4
35.6
62.3
48.7
75
41.8
23.7
76.8
24
23.9
62.5
42.7
23.4
23.3
48.7
65.1
34.6
24.5
34.9
76.5
57.8
22.7
56.5
24.5
23.2
46.8
76.6
75.9
47.4
25.3
27.2
66
28.1
22.5
22.7
23.4
58.5
35.5
24.8
1.130
0.884
1.148
1.093
57
31
31
57
48
67
40
23
67
23
23
57
40
23
23
40
57
31
23
31
67
48
23
48
23
23
40
67
67
48
23
31
57
31
23
23
23
57
31
23
34
52
30
42
36
36
32
32
49
30
41
52
30
32
32
44
27
31
32
44
43
48
36
30
41
22
35
44
52
45
29
25
35
26
23
27
22
45
27
24
1.014
1.120
1.046
1.029
1.147
1.044
1.041
1.096
1.067
1.016
1.012
1.217
1.142
1.116
1.065
1.125
1.142
1.204
0.987
1.177
1.064
1.010
1.171
1.144
1.133
0.987
1.101
0.878
1.158
0.907
0.980
0.985
1.017
1.026
1.144
1.078
Performance Service Gender Raise
Rating
85
80
75
100
90
70
100
90
100
80
100
95
100
90
80
90
55
80
85
70
95
65
65
75
70
95
80
95
95
90
60
95
90
80
90
75
95
95
90
90
8
7
5
16
16
12
8
9
10
7
19
22
2
12
8
4
3
11
1
16
13
6
6
9
4
2
7
9
5
18
4
4
9
2
4
3
2
11
6
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
5.7
3.9
3.6
5.5
5.7
4.5
5.7
5.8
4
4.7
4.8
4.5
4.7
6
4.9
5.7
3
5.6
4.6
4.8
6.3
3.8
3.3
3.8
4
6.2
3.9
4.4
5.4
4.3
3.9
5.6
5.5
4.9
5.3
4.3
6.2
4.5
5.5
6.3
41
42
43
44
45
46
47
48
49
50
45.8
22.2
77.4
58.8
51.2
61.3
64.3
67.6
61.3
66.1
1.144
0.965
1.155
1.032
1.066
1.076
1.128
1.186
1.075
1.159
40
23
67
57
48
57
57
57
57
57
25
32
42
45
36
39
37
34
41
38
80
100
95
90
95
75
95
90
95
80
5
8
20
16
8
20
5
11
21
12
0
1
1
0
1
0
0
1
0
0
4.3
5.7
5.5
5.2
5.2
3.9
5.5
5.3
6.6
4.6
Degree Gender
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
M
M
F
M
M
M
F
F
M
F
F
M
F
F
F
M
F
F
M
F
M
F
F
F
M
F
M
F
M
M
F
M
M
M
F
F
F
M
F
M
Gr
E
B
B
E
D
F
C
A
F
A
A
E
C
A
A
C
E
B
A
B
F
D
A
D
A
A
C
F
F
D
A
B
E
B
A
A
A
E
B
A
The ongoing question that the weekly assignments will focus on is: Are males and fema
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equa
The column labels in the table mean:
ID – Employee sample number
Salary – Salary in thousands
Age – Age in years
Performance Rating – Appraisal rating (emp
Service – Years of service (rounded) Gender – 0 = male, 1 = female
Midpoint – salary grade midpoint
Raise – percent of last raise
Grade – job/pay grade
Degree (0= BSBA 1 = MS)
Gender1 (Male or Female)
Compa – salary divided by midpoint
0
1
0
1
1
1
1
1
0
0
M
F
F
M
F
M
M
F
M
M
C
A
F
E
D
E
E
E
E
E
s on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
each grade comprise equal work.
thousands
ng – Appraisal rating (employee evaluation score)
, 1 = female
vided by midpoint
Sal
Compa
24
1.045
24.2
1.053
23.4
1.018
23.4
1.017
22.6
22.9
23.1
23.3
22.7
23.5
0.983
0.995
1.003
1.011
0.985
1.023
23
24
35.5
1.002
1.042
1.145
34.7
35.5
35.2
40.4
42.7
53.4
1.119
1.146
1.136
1.01
1.068
1.112
51.5
49.8
68.3
65.4
78.4
75.9
1.072
1.037
1.198
1.148
1.17
1.133
24
23.3
24.1
27.5
27.1
27.7
1.044
1.012
1.049
0.887
0.875
0.895
40.8
43.9
41
1.019
1.097
1.025
48.7
49.4
64.4
64.5
58.9
57.9
1.014
1.029
1.13
1.132
1.033
1.016
59
63.3
56.8
58
1.035
1.111
0.996
1.017
G
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Mid
23
23
23
23
23
23
23
23
23
23
23
23
31
31
31
31
40
40
48
48
48
57
57
67
67
23
23
23
31
31
31
40
40
40
48
48
57
57
57
57
57
57
57
57
Age
32
30
41
32
32
36
22
29
23
27
22
32
30
31
44
27
32
30
48
30
36
27
34
44
42
32
41
24
52
25
26
44
35
25
36
45
34
42
52
35
45
45
39
37
EES
90
80
100
90
80
65
95
60
90
75
95
100
75
80
70
90
100
100
65
75
95
55
90
95
95
85
70
90
80
95
80
90
80
80
90
90
85
100
95
90
95
90
75
95
SR
9
7
19
12
8
6
2
4
4
3
2
8
5
11
16
6
8
2
6
9
8
3
11
9
20
1
4
2
7
4
2
4
7
5
16
18
8
16
22
9
11
16
20
5
G
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Raise
5.8
4.7
4.8
6
4.9
3.3
6.2
3.9
5.3
4.3
6.2
5.7
3.6
5.6
4.8
5.5
5.7
4.7
3.8
3.8
5.2
3
5.3
4.4
5.5
4.6
4
6.3
3.9
5.6
4.9
5.7
3.9
4.3
5.7
4.3
5.7
5.5
4.5
5.5
4.5
5.2
3.9
5.5
Deg
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
62.4
63.8
79
77
74.8
1.094
1.12
1.179
1.149
1.116
76
1.135
0
0
0
0
0
0
57
57
67
67
67
67
41
38
36
49
43
52
95
80
70
100
95
95
21
12
12
10
13
5
0
0
0
0
0
0
6.6
4.6
4.5
4
6.3
5.4
0
0
1
1
1
0
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.705018
R Square
0.49705
Adjusted R 0.413225
Standard E 0.056125
Observatio
50
ANOVA
df
Regression
Residual
Total
SS
MS
Significance F
7 0.13075 0.018679 5.929623 7.83E-05
42 0.132302 0.00315
49 0.263052
Coefficients
Standard Error t Stat
Intercept 0.948624 0.081717 11.60868
Mid
0.0035 0.000649 5.390013
Age
0.000553 0.001446 0.382293
EES
-0.001846 0.001025 -1.800846
SR
G
Raise
Deg
F
P-value Lower 95%Upper 95%
Lower 95.0%
Upper 95.0%
1.09E-14 0.783713 1.113535 0.783713 1.113535
2.98E-06 0.002189 0.00481 0.002189 0.00481
0.704172 -0.002365 0.003471 -0.002365 0.003471
0.078911 -0.003915 0.000223 -0.003915 0.000223
-0.000418 0.001828 -0.228814 0.820124 -0.004107 0.00327 -0.004107 0.00327
0.064665 0.01834 3.525963 0.001035 0.027654 0.101676 0.027654 0.101676
0.014655 0.013909 1.053639 0.298072 -0.013414 0.042724 -0.013414 0.042724
0.001468 0.01611
0.0911 0.927847 -0.031043 0.033979 -0.031043 0.033979
t-Test: Two-Sample Assuming Equal Variances
Variable 1 Variable 2
Mean
1.06684 1.04836
Variance 0.004302 0.006481
Observatio
25
25
Pooled Var 0.005391
Hypothesiz
0
df
48
t Stat
0.889835
P(T<=t) one0.188996
t Critical on 1.677224
P(T<=t) two0.377993
t Critical tw 2.010635
Upper 95.0%
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.993129
R Square 0.986305
Adjusted R 0.984022
Standard E 2.435282
Observatio
50
ANOVA
df
Regression
Residual
Total
SS
MS
F
Significance F
7 17938.42 2562.632 432.1034
42 249.0852
5.9306
49 18187.51
5.3E-37
Coefficients
Standard Error t Stat
Intercept -4.871454 3.545701 -1.373905
Mid
1.228416 0.028171 43.60516
Age
0.036828 0.06274 0.586996
EES
-0.082158 0.044484 -1.846901
P-value Lower 95%Upper 95%
Lower 95.0%
Upper 95.0%
0.17676 -12.02697 2.284059 -12.02697 2.284059
1.32E-36 1.171563 1.285268 1.171563 1.285268
0.560349 -0.089786 0.163442 -0.089786 0.163442
0.071815 -0.171931 0.007615 -0.171931 0.007615
SR
G
Raise
Deg
0.331925 -0.2379
0.000694 1.308599
0.268799 -0.541601
0.960865 -1.376149
-0.077848
2.914508
0.676329
0.034504
0.079309 -0.981585
0.795761 3.662545
0.603509 1.120662
0.699007 0.049362
0.082203 -0.2379
4.520418 1.308599
1.894259 -0.541601
1.445158 -1.376149
0.082203
4.520418
1.894259
1.445158
Upper 95.0%
...
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