A. State the claim. B. State the test used and any necessary assumptions to cond
ID: 3225168 • Letter: A
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.
Do students who use support services graduate faster or have higher College GPA’s on average at a 5% level of significance? Test these 2 claims.
They are also interested in whether ACT scores or H.S. GPA’s are correlated to the students collegiate GPA. In addition if there is a correlation, how can they model the correlation at a 5% level of significance?
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.
Does the mean collegiate GPA differ by residential Region at a 5% level of significance?
Records indicate that Region A is 15% region B is 60% and Region C is 25%. Is there enough evidence to support this claim at a 5% level of significance?
A Dean of support services believes the proportion of students using support service is more than 30%. Does the data support this claim at a 5% level of significance?
Is there evidence to support that on average student GPA’s increased due to use of support services at a 5% level of significance?
Based on the tests performed what is your recommendation to administration concerning whether Support services are beneficial to students?
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
HYPOTHESIS TESTING CASE STUDY 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.
Do students who use support services graduate faster or have higher College GPA’s on average at a 5% level of significance? Test these 2 claims.
They are also interested in whether ACT scores or H.S. GPA’s are correlated to the students collegiate GPA. In addition if there is a correlation, how can they model the correlation at a 5% level of significance?
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.
Does the mean collegiate GPA differ by residential Region at a 5% level of significance?
Records indicate that Region A is 15% region B is 60% and Region C is 25%. Is there enough evidence to support this claim at a 5% level of significance?
A Dean of support services believes the proportion of students using support service is more than 30%. Does the data support this claim at a 5% level of significance?
Is there evidence to support that on average student GPA’s increased due to use of support services at a 5% level of significance?
Based on the tests performed what is your recommendation to administration concerning whether Support services are beneficial to students?
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
22
3.92
5
C
Y
3.61
3
3
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
3.3
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
3.4
6
B
N
22
2.31
26
2.28
5
B
N
23
3.37
26
3.29
4
A
N
24
2.3
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
24
3.27
5
C
N
29
2
31
2.32
5.5
C
Y
1.85
30
2.8
21
2.72
4.5
A
N
31
2.49
23
2.67
6
B
Y
2.19
32
3.73
23
3
5
C
N
33
2.36
24
2.15
4
A
N
34
3.6
31
4
4.5
B
N
35
3.43
21
3.3
5
A
N
36
1.46
18
2.25
4
A
Y
1.93
37
4
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
Solution:
Question1: Do students who use support services graduate faster?
A. State the claim.
Do students who use support services graduate faster?
B. State the test used and any necessary assumptions to conduct the test.
We use 2-sample t-test one tailed
Assumptions:
1) Normality
2) Iid
3) Homoskedasticity
C. State the hypothesis in words relating to the question and as symbols.
H0: who use support services graduate faster i.e. NY(Non-support)<= NY(support)
Ha: NY(Non-support)>NY(support)
Where NY: Number of years took to Graduate
D. State the probability distribution used to find critical values.
t- DISTRIBUTION
E. State the test statistic(Value)
t-stat=0.922
(using excel data add in)
t-stat = {mean of NY(Non-support)- mean of NY(support)}/ std error
F. State if you reject or fail to reject the null hypothesis, support with p-value or traditional test.
p-value=0.18>0.05; cant reject H0
G. State your conclusion in terms of the claim.
Students who use support services don’t get graduate faster
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.
Yes we will be committing type I error if we reject H0.
Question2: Do students who use support get more CGPA?
From A to E all remains same as in Q1.
F. p-value=0.12>0.05; cant reject H0
G. Claim is invalid
Question3: Do They are also interested in whether ACT scores or H.S. GPA’s are correlated to the students collegiate GPA.?
Correlation between ACT score & College CGPA
0.189562
Correlation between HS CGPA & College CGPA
0.740916
Question4: if there is a relationship between residence region and participation in support services at a 5% level of significance..?
We used chi-sq test for independence
H0: no relationship
Ha: there exists a relationship
Assumption: Non-parametric test with integer numbers
Y N
A 5 7 12
B 9 6 15
C 7 6 13
21 19 40
expected
Y N
A 6.3 5.7 12
B 7.875 7.125 15
C 6.825 6.175 13
21 19 40
chi-sq
Y N
A 0.268253968 0.296491228
B 0.160714286 0.177631579
C 0.004487179 0.004959514
chi-sq 0.912537755
p-value= 0.633643443 >0.05 cant reject H0; no relationship between region & support
Excel formula:
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
22
3.92
5
C
Y
3.61
3
3
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
3.3
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
3.4
6
B
N
22
2.31
26
2.28
5
B
N
23
3.37
26
3.29
4
A
N
24
2.3
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
24
3.27
5
C
N
29
2
31
2.32
5.5
C
Y
1.85
30
2.8
21
2.72
4.5
A
N
31
2.49
23
2.67
6
B
Y
2.19
32
3.73
23
3
5
C
N
33
2.36
24
2.15
4
A
N
34
3.6
31
4
4.5
B
N
35
3.43
21
3.3
5
A
N
36
1.46
18
2.25
4
A
Y
1.93
37
4
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
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