4. Based on our sample data, can we conclude that males and females are distribu
ID: 3394614 • Letter: 4
Question
4. Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?
What are the hypothesis statements:
Ho:
Ha:
Do manual calculations per cell here (if desired)
A
B
C
D
E
F
A
B
C
D
E
F
OBS COUNT - m
M
OBS COUNT - f
F
Sum =
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?
What does this decision mean for our equal pay question:
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
A
B
C
D
E
F
A
B
C
D
E
F
OBS COUNT - m
M
OBS COUNT - f
F
Sum =
EXPECTED
Explanation / Answer
Based on our sample data, can we conclude that males and females are distributed across grades in a similar pattern within the population?
What are the hypothesis statements:
Ho: Males and females are distributed across grades in a similar pattern within the population
Ha: Males and females are distributed across grades in a different pattern within the population
Observed Frequencies
Gender1
A
B
C
D
E
F
Total
Male
3
3
3
2
10
4
25
Female
12
4
2
3
2
2
25
Total
15
7
5
5
12
6
50
Expected Frequencies
Gender1
A
B
C
D
E
F
Total
Male
7.5
3.5
2.5
2.5
6
3
25
Female
7.5
3.5
2.5
2.5
6
3
25
Total
15
7
5
5
12
6
50
Calculations
fo-fe
-4.5
-0.5
0.5
-0.5
4
1
4.5
0.5
-0.5
0.5
-4
-1
(fo-fe)^2/fe
2.7000
0.0714
0.1000
0.1000
2.6667
0.3333
2.7000
0.0714
0.1000
0.1000
2.6667
0.3333
Level of Significance
0.05
Number of Rows
2
Number of Columns
6
Degrees of Freedom
5
Results
Critical Value
11.070
Chi-Square Test Statistic
11.9429
p-Value
0.0356
Reject the null hypothesis
What is the value of the chi square statistic: 11.9429
What is the p-value associated with this value: 0.0356
Is the p-value <0.05? yes
Do you reject or not reject the null hypothesis: yes, rejected the null hypothesis
If you rejected the null, what is the Phi correlation: 0.489
What does this correlation mean?
There is significant association between gender and grades .
Observed Frequencies
Gender1
A
B
C
D
E
F
Total
Male
3
3
3
2
10
4
25
Female
12
4
2
3
2
2
25
Total
15
7
5
5
12
6
50
Expected Frequencies
Gender1
A
B
C
D
E
F
Total
Male
7.5
3.5
2.5
2.5
6
3
25
Female
7.5
3.5
2.5
2.5
6
3
25
Total
15
7
5
5
12
6
50
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