For each question: A.State the claim. B.State the test used and any necessary as
ID: 3225264 • 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.
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?
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
Total number of students = 40
Number of students using support service = 19
p = 19/40 = 0.475
i.) A Dean of support services believes the proportion of students using support service is more than 30%.
ii.) t-test for porportions will be used.
Assumptions are:
iii.) Null hypothesis will be opposite of what the calim is, i.e. There are lss than or equal to 30% students that re using support serviec.
H0: p 0.3
H1: p > 0.3
iv.) t-distribution will be used to find critical values
v.) p = 0.475
1 - p = 0.525
SE = p*(1-p)/n
= 0.0789
t = (0.3-0.475) / SE = -2.84
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