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 Solution 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 Obs.

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. E
F
A
B
C
D
E
F
OBS COUNT - m
M
OBS COUNT - f
F
Sum =
EXPECTED
Solution
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

20. 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

21. 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

22. 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

23. 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

24. 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