Homework Sourse4 Based on our sample data can we conclude that males and fe
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
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 |
