E & J College is doing a study on their policies. After randomly gathering data
ID: 3225352 • Letter: E
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
State the claim. State the test used and any necessary assumptions to conduct the test. State the hypothesis in words relating to the question and as symbols. State the probability distribution used to find critical values. State the test statistic(Value) State if you reject or fail to reject the null hypothesis, support with p-value or traditional test. State your conclusion in terms of the claim. 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.
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
H0: 1 - 2 = 0 i.e. (1 = 2) (There is no difference in years to graduate amongst Students who use support services and who do not)
H1: 1 - 2 0 i.e. (1 2) (There is difference in years to graduate amongst Students who use support services and who do not)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (19-1)*1.065^2+(21-1)*0.80^2/18+20
= 20.41605+12.8/38
=0.87
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(4.87-4.6)-0/0.87(1/19+1/21)
=0.27/0.9605
=0.2811
tCRIT is 2.0244 and hence we cannot reject the null hypothesis. Hence, we conclude that there is no difference in years to graduate amongst Students who use support services and who do not.
b)
H0: 1 <= 2 = 0 (Students who receive support services either have lower or equal GPA to those who do not receive support services)
H1: 1 > 2 0 (Students who receive support services have higher GPA to those who do not receive support services)
Assuming population variances are equal, we would have to calculate pooled-variance t-Test
Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)
= (19-1)*0.47^2+(21-1)*0.54^2/18+20
= 3.9762+5.832/38
=0.2581
tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)
=(2.75-2.94)-0/0.2581(1/19+1/21)
=-0.19/0.1609
=-1.18
tCRIT is 1.6859 and hence we cannot reject the null hypothesis. Hence, we conclude that students who receive support services have higher GPA to those who do not receive support services.
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