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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.