For each question: State the claim. State the test used and any necessary assump
ID: 3225394 • Letter: F
Question
For each question:
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.
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.
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
Part-1
We have to test the claim that the proportion of students using support service is more than 30%
Null hypothesis H0: p<=,0.30 and alternative Ha:p>0.30
The assumption is that np>5 and n(1-p)>5
Here n=40 and so np=40*0.3=12>5 and n(1-p)=40*(1-0.3)=28>5 so assumption satisfied.
We use Z-distribution and the test statistic is Z=(phat-0.3)/sqrt(0.3*(1-0.3)/40)
We have phat=19/40=0.475
So, Z=(0.475-0.30)/sqrt(0.30*(1-0.30)/40) =2.42
Row Labels
Count of Participated in Support Service Program
N
21
Y
19
Grand Total
40
p-value=P(Z>2.42)=0.0078 using excel function =1-NORMSDIST(2.42)
As p-value<0.05, we reject the null hypothesis and conclude that the proportion of students using support service is more than 30%. As we reject the null hypothesis so it may be the case that true proportion is in fact <=0.30 in that case we commit Type-I error.
Part-2
We have to test the claim that on average student GPA’s increased due to use of support services at a 5% level of significance.
Null hypothesis H0: µd<=0 and alternative Ha: µd>0 , where µd is the GPAafter-GPAbefore for Support=Y.
The assumption is that difference is normally distributed.
We use t-distribution and the test statistic is t=(0.38-0)/(0.20/sqrt(19))=8.28
We have
Average of Difference
StdDev of Difference
Count of Difference
0.376842105
0.203662374
19
Degree of freedom =n-1=19
p-value=7.48163E-08 using excel function =TDIST(8.28,18,1)
As p-value<0.05, we reject the null hypothesis and conclude that on average student GPA’s increased due to use of support services at a 5% level of significance. As we reject the null hypothesis so it may be the case that true mean difference is <=0 in that case we commit Type-I error.
Row Labels
Count of Participated in Support Service Program
N
21
Y
19
Grand Total
40
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