Homework Sourse2 Using our sample data construct a 95 confidence interval f
2. Using our sample data, construct a 95% confidence interval for the mean salary difference between the genders in the population. How does this compare to the findings in week 2, question 2?
Difference
St Err.
T value
Low
to
High
Can the means be equal? Yes or No. Why?
Why is using a two sample tool (t-test, confidence interval) a better choice than using 2 one-sample techniques when comparing two samples?
ID
Salary
Compa
Midpoint
Age
Performance Rating
Service
Gender
Raise
Degree
Gender1
Gr
1
66.1
1.159
57
34
85
8
0
5.7
0
M
E
2
25.9
0.834
31
52
80
7
0
3.9
0
M
B
3
35.2
1.135
31
30
75
5
1
3.6
1
F
B
4
55.3
0.971
57
42
100
16
0
5.5
1
M
E
5
49.6
1.033
48
36
90
16
0
5.7
1
M
D
6
78.3
1.168
67
36
70
12
0
4.5
1
M
F
7
42.3
1.058
40
32
100
8
1
5.7
1
F
C
8
22.8
0.990
23
32
90
9
1
5.8
1
F
A
9
78
1.164
67
49
100
10
0
4
1
M
F
10
23.3
1.014
23
30
80
7
1
4.7
1
F
A
11
23.6
1.025
23
41
100
19
1
4.8
1
F
A
12
60.8
1.067
57
52
95
22
0
4.5
0
M
E
13
40.6
1.014
40
30
100
2
1
4.7
0
F
C
14
21.7
0.943
23
32
90
12
1
6
1
F
A
15
21.8
0.949
23
32
80
8
1
4.9
1
F
A
16
37.4
0.934
40
44
90
4
0
5.7
0
M
C
17
57
1.000
57
27
55
3
1
3
1
F
E
18
33.5
1.081
31
31
80
11
1
5.6
0
F
B
19
23
1.000
23
32
85
1
0
4.6
1
M
A
20
36
1.162
31
44
70
16
1
4.8
0
F
B
21
76
1.135
67
43
95
13
0
6.3
1
M
F
22
43.7
0.911
48
48
65
6
1
3.8
1
F
D
23
25.3
1.098
23
36
65
6
1
3.3
0
F
A
24
48.9
1.019
48
30
75
9
1
3.8
0
F
D
25
25.8
1.122
23
41
70
4
0
4
0
M
A
26
23.3
1.013
23
22
95
2
1
6.2
0
F
A
27
42.3
1.057
40
35
80
7
0
3.9
1
M
C
28
75.2
1.122
67
44
95
9
1
4.4
0
F
F
29
80.9
1.208
67
52
95
5
0
5.4
0
M
F
30
49
1.020
48
45
90
18
0
4.3
0
M
D
31
24.2
1.054
23
29
60
4
1
3.9
1
F
A
32
27.5
0.886
31
25
95
4
0
5.6
0
M
B
33
63.6
1.115
57
35
90
9
0
5.5
1
M
E
34
28.6
0.922
31
26
80
2
0
4.9
1
M
B
35
22.4
0.976
23
23
90
4
1
5.3
0
F
A
36
23.6
1.026
23
27
75
3
1
4.3
0
F
A
37
24.3
1.057
23
22
95
2
1
6.2
0
F
A
38
63
1.105
57
45
95
11
0
4.5
0
M
E
39
34.8
1.123
31
27
90
6
1
5.5
0
F
B
40
24.3
1.057
23
24
90
2
0
6.3
0
M
A
41
42.8
1.071
40
25
80
5
0
4.3
0
M
C
42
23
0.998
23
32
100
8
1
5.7
1
F
A
43
75.4
1.125
67
42
95
20
1
5.5
0
F
F
44
60.7
1.065
57
45
90
16
0
5.2
1
M
E
45
57.9
1.206
48
36
95
8
1
5.2
1
F
D
46
62.2
1.091
57
39
75
20
0
3.9
1
M
E
47
62.2
1.091
57
37
95
5
0
5.5
1
M
E
48
70.1
1.230
57
34
90
11
1
5.3
1
F
E
49
61.7
1.083
57
41
95
21
0
6.6
0
M
E
50
61.4
1.077
57
38
80
12
0
4.6
0
M
E
| Difference | St Err. | T value | Low | to | High |
Solution
Two-sample T for Salary
Gender N Mean StDev SE Mean
0 25 52.3 18.6 3.7
1 25 37.2 17.5 3.5
Difference = mu (0) - mu (1)
Estimate for difference: 15.06
95% CI for difference: (4.77, 25.35)
T-Test of difference = 0 (vs not =): T-Value = 2.94 P-Value = 0.005 DF = 48
Difference = 15.06
standard error of difference between means = 5.107
T value = 2.94
Low = 4.77
High =25.35
No, The means are not equal . ( since P-value is very low i.e. 0005)
We use two sample t-test to the average salary differences between the two genders. This gives whether there is truly difference exists between the genders . If we use one sample individual test, then this test gives the individual averages confidence interval , from which we can\'t interpret the difference of their averages.
