For each question: A.State the claim. B.State the test used and any necessary as
ID: 3225262 • Letter: F
Question
For each question:
A.State the claim.
B.State the test used and any necessary assumptions to conduct the test.
C.State the hypothesis in words relating to the question and as symbols.
D.State the probability distribution used to find critical values.
E.State the test statistic(Value)
F.State if you reject or fail to reject the null hypothesis, support with p-value or traditional test.
G.State your conclusion in terms of the claim.
H.Determine if there is a chance of a Type I or a Type II error, then state what the possible error may be in terms of the question
E & J College is doing a study on their policies. After randomly gathering data from a sample of 40 graduates, they put the raw data in a table and did not now how to proceed. They are asking for your statistical expertise to provide an analysis. They need you to answer the following questions. Assume all populations are normally distributed and these are random samples.
3) In addition, they would like to know if there is a relationship between residence region and participation in support services at a 5% level of significance.
Here is the table:
Subject
HS GPA
ACT Score
College G.P.A
Number of years took to Graduate
Residential Region
Participated in Support Service Program
GPA Before Support Services
1
2.05
29
2.38
5.5
B
N
2
4.00
22
3.92
5
C
Y
3.61
3
3.00
26
3.51
4
B
Y
3.23
4
3.89
24
3.57
5
C
Y
3.03
5
3.36
20
3.78
5
C
N
6
3.08
25
2.39
3.5
A
Y
2.06
7
3.28
25
3.11
5.5
B
N
8
1.69
16
2.38
4
B
N
9
2.17
23
2.59
3
C
N
10
3.06
27
3.31
5
B
N
11
2.77
22
2.29
4
B
Y
1.65
12
2.14
21
2.78
8
B
Y
2.09
13
2.03
25
2.63
5
B
Y
2.36
14
2.73
24
2.66
6
A
Y
2.43
15
2.82
25
2.44
5
C
N
16
3.77
29
3.30
4
B
N
17
2.51
21
2.08
3
C
N
18
2.88
22
2.86
3.5
C
Y
2.64
19
3.37
25
2.55
4.5
A
Y
2.51
20
2.39
22
2.42
5.5
A
Y
1.97
21
3.15
21
3.40
6
B
N
22
2.31
26
2.28
5
B
N
23
3.37
26
3.29
4
A
N
24
2.30
19
2.52
4.5
A
Y
2.56
25
3.53
22
3.17
5
C
Y
2.67
26
3.43
23
2.57
4
B
N
27
2.58
23
2.46
4
A
Y
2.26
28
4.00
24
3.27
5
C
N
29
2.00
31
2.32
5.5
C
Y
1.85
30
2.80
21
2.72
4.5
A
N
31
2.49
23
2.67
6
B
Y
2.19
32
3.73
23
3.00
5
C
N
33
2.36
24
2.15
4
A
N
34
3.60
31
4.00
4.5
B
N
35
3.43
21
3.30
5
A
N
36
1.46
18
2.25
4
A
Y
1.93
37
4.00
28
3.41
4
A
N
38
3.57
31
2.79
5
B
Y
2.22
39
2.74
21
2.99
5.5
C
N
40
2.37
22
2.48
4.5
C
Y
1.82
Subject
HS GPA
ACT Score
College G.P.A
Number of years took to Graduate
Residential Region
Participated in Support Service Program
GPA Before Support Services
1
2.05
29
2.38
5.5
B
N
2
4.00
22
3.92
5
C
Y
3.61
3
3.00
26
3.51
4
B
Y
3.23
4
3.89
24
3.57
5
C
Y
3.03
5
3.36
20
3.78
5
C
N
6
3.08
25
2.39
3.5
A
Y
2.06
7
3.28
25
3.11
5.5
B
N
8
1.69
16
2.38
4
B
N
9
2.17
23
2.59
3
C
N
10
3.06
27
3.31
5
B
N
11
2.77
22
2.29
4
B
Y
1.65
12
2.14
21
2.78
8
B
Y
2.09
13
2.03
25
2.63
5
B
Y
2.36
14
2.73
24
2.66
6
A
Y
2.43
15
2.82
25
2.44
5
C
N
16
3.77
29
3.30
4
B
N
17
2.51
21
2.08
3
C
N
18
2.88
22
2.86
3.5
C
Y
2.64
19
3.37
25
2.55
4.5
A
Y
2.51
20
2.39
22
2.42
5.5
A
Y
1.97
21
3.15
21
3.40
6
B
N
22
2.31
26
2.28
5
B
N
23
3.37
26
3.29
4
A
N
24
2.30
19
2.52
4.5
A
Y
2.56
25
3.53
22
3.17
5
C
Y
2.67
26
3.43
23
2.57
4
B
N
27
2.58
23
2.46
4
A
Y
2.26
28
4.00
24
3.27
5
C
N
29
2.00
31
2.32
5.5
C
Y
1.85
30
2.80
21
2.72
4.5
A
N
31
2.49
23
2.67
6
B
Y
2.19
32
3.73
23
3.00
5
C
N
33
2.36
24
2.15
4
A
N
34
3.60
31
4.00
4.5
B
N
35
3.43
21
3.30
5
A
N
36
1.46
18
2.25
4
A
Y
1.93
37
4.00
28
3.41
4
A
N
38
3.57
31
2.79
5
B
Y
2.22
39
2.74
21
2.99
5.5
C
N
40
2.37
22
2.48
4.5
C
Y
1.82
Explanation / Answer
As both residence region and participation in support services at are categorical variables, so to know the relationship between them we will apply Chi-square test of independence.
A. We claim that the participation in support services depends on residence region
B. We will use chi-square test of independence and main assumption is that each expected count or more than 80% expected counts are greater than 5.
C. Null Hypothesis H0 : Participation in support services is independent of residence region
Alternative Hypothesis Ha : Participation in support services depends on residence region
D. We will use chi-square distribution to find the critical values.
E. From following results Test statistic 2=0.91
Chi-Square Test
Observed Frequencies
Participated in Support Service Program
Calculations
Residential Region
A
B
C
Total
fo-fe
N
5
9
7
21
-1.3
1.125
0.175
Y
7
6
6
19
1.3
-1.125
-0.175
Total
12
15
13
40
Expected Frequencies
Participated in Support Service Program
Residential Region
A
B
C
Total
(fo-fe)^2/fe
N
6.3
7.875
6.825
21
0.268253968
0.160714286
0.004487179
Y
5.7
7.125
6.175
19
0.296491228
0.177631579
0.004959514
Total
12
15
13
40
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991464547
Chi-Square Test Statistic
0.912537755
p-Value
0.633643442
Do not reject the null hypothesis
Expected frequency assumption
is met.
F. As p-value=0.6336>0.05, we do not reject the null hypothesis.
G. We conclude that Participation in support services is independent of residence region
H. As we accepted the null, so it may be the case that null is false in which case we make Type-II error.
Chi-Square Test
Observed Frequencies
Participated in Support Service Program
Calculations
Residential Region
A
B
C
Total
fo-fe
N
5
9
7
21
-1.3
1.125
0.175
Y
7
6
6
19
1.3
-1.125
-0.175
Total
12
15
13
40
Expected Frequencies
Participated in Support Service Program
Residential Region
A
B
C
Total
(fo-fe)^2/fe
N
6.3
7.875
6.825
21
0.268253968
0.160714286
0.004487179
Y
5.7
7.125
6.175
19
0.296491228
0.177631579
0.004959514
Total
12
15
13
40
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991464547
Chi-Square Test Statistic
0.912537755
p-Value
0.633643442
Do not reject the null hypothesis
Expected frequency assumption
is met.
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