Project #36966 - stats

Question 1

.    In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

.    X1

.    X12

.    X2

.    X22

.    1

.    1

.    7

.    49

.    3

.    9

.    7

.    49

.    3

.    9

.    9

.    81

.    2

.    4

.    5

.    25

.    4

.    16

.    5

.    25

.    2

.    4

.    8

.    64

.    1

.    1

.    6

.    36

.    4

.    16

.    7

.    49

.    ΣX1=20

.    ΣX12=60

.    ΣX2=54

.    ΣX22=378

.    (ΣX1)2=400

.     

.    X2)2=2916

.     

.    M1 = 2.50

.     

.    M2 = 6.75

.     

.    s1 = 1.20

.     

.    s2 = 1.39

.     

.    SS1 = 10.00

.     

.    SS2 = 13.50

.     

.    Is this a between-groups or a within-groups research design?


.    


. 

.    a.

.    within-groups


. 

.    b.

.    between-groups


Question 2

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

X1

X12

X2

X22

1

1

7

49

3

9

7

49

3

9

9

81

2

4

5

25

4

16

5

25

2

4

8

64

1

1

6

36

4

16

7

49

ΣX1=20

ΣX12=60

ΣX2=54

ΣX22=378

(ΣX1)2=400

 

X2)2=2916

 

M1 = 2.50

 

M2 = 6.75

 

s1 = 1.20

 

s2 = 1.39

 

SS1 = 10.00

 

SS2 = 13.50

 

 

 

Based on the research design you identified for this hypothesis test, what is the appropriate statistical analysis?

 

a.

t-test for independent samples

 

b.

t-test for related samples

 

c.

one sample t-test

Question 3

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

Identify the independent variable in this study.

 

a.

The time of day the evidence was presented in the court room.

 

b.

The length of the jail sentence in years.

 

c.

The court room in which the evidence was presented.

 

d.

The information given concerning the evidence.

Question 4

What is the measurement scale of the independent variable?

 

a.

interval

 

b.

ratio

 

c.

ordinal

 

d.

nominal

Question 5

.    In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.
Identify the dependent variable in this study.



. 

.    a.

.    The time of day the evidence was presented in the court room.


. 

.    b.

.    The length of the jail sentence in years.


. 

.    c.

.    The information given concerning the evidence.


. 

.    d.

.    The court room in which the evidence was presented.

 

Question 6

What is the measurement scale of the dependent variable?

 

a.

ratio

 

b.

interval

 

c.

ordinal

 

d.

nominal

Question 7

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

X1

X12

X2

X22

1

1

7

49

3

9

7

49

3

9

9

81

2

4

5

25

4

16

5

25

2

4

8

64

1

1

6

36

4

16

7

49

ΣX1=20

ΣX12=60

ΣX2=54

ΣX22=378

(ΣX1)2=400

 

X2)2=2916

 

M1 = 2.50

 

M2 = 6.75

 

s1 = 1.20

 

s2 = 1.39

 

SS1 = 10.00

 

SS2 = 13.50

 

 

What is the null hypothesis (H0) for this study?

 

a.

μ1-μ2 ≠ 0.00

 

b.

μD ≠ 0.00

 

c.

μ1-μ2 = 0.00

 

d.

μD = 0.00

 

Question 8

.    In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

.    X1

.    X12

.    X2

.    X22

.    1

.    1

.    7

.    49

.    3

.    9

.    7

.    49

.    3

.    9

.    9

.    81

.    2

.    4

.    5

.    25

.    4

.    16

.    5

.    25

.    2

.    4

.    8

.    64

.    1

.    1

.    6

.    36

.    4

.    16

.    7

.    49

.    ΣX1=20

.    ΣX12=60

.    ΣX2=54

.    ΣX22=378

.    (ΣX1)2=400

.     

.    X2)2=2916

.     

.    M1 = 2.50

.     

.    M2 = 6.75

.     

.    s1 = 1.20

.     

.    s2 = 1.39

.     

.    SS1 = 10.00

.     

.    SS2 = 13.50

.     

.     

.    What is the alternative hypothesis (H1) for this study?



. 

.    a.

.    μD ≠ 0.00


. 

.    b.

.    μD = 0.00


. 

.    c.

.    μ1-μ2 = 0.00


. 

.    d.

.    μ1-μ2 ≠ 0.00


.    




 

Question 9

.    In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

.    X1

.    X12

.    X2

.    X22

.    1

.    1

.    7

.    49

.    3

.    9

.    7

.    49

.    3

.    9

.    9

.    81

.    2

.    4

.    5

.    25

.    4

.    16

.    5

.    25

.    2

.    4

.    8

.    64

.    1

.    1

.    6

.    36

.    4

.    16

.    7

.    49

.    ΣX1=20

.    ΣX12=60

.    ΣX2=54

.    ΣX22=378

.    (ΣX1)2=400

.     

.    X2)2=2916

.     

.    M1 = 2.50

.     

.    M2 = 6.75

.     

.    s1 = 1.20

.     

.    s2 = 1.39

.     

.    SS1 = 10.00

.     

.    SS2 = 13.50

.     

.     

.    What is the df value to determine the critical value for this study?



 

.                 

.    a.

.    15


.                 

.    b.

.    14


.                 

.    c.

.    7


.                 

.    d.

.    6


Question 10

What is the tcritical value for this study?

 

a.

+ 2.131

 

b.

+ 2.145

 

c.

+ 2.447

 

d.

+ 2.365

 

  

 

 

 

 

 

 

 

 

 

 

Question 11

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

X1

X12

X2

X22

1

1

7

49

3

9

7

49

3

9

9

81

2

4

5

25

4

16

5

25

2

4

8

64

1

1

6

36

4

16

7

49

ΣX1=20

ΣX12=60

ΣX2=54

ΣX22=378

(ΣX1)2=400

 

X2)2=2916

 

M1 = 2.50

 

M2 = 6.75

 

s1 = 1.20

 

s2 = 1.39

 

SS1 = 10.00

 

SS2 = 13.50

 

 

Pooled variance = ?

 

a.

2.94

 

b.

1.47

 

c.

1.68

 

d.

3.36

Question 12

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

X1

X12

X2

X22

1

1

7

49

3

9

7

49

3

9

9

81

2

4

5

25

4

16

5

25

2

4

8

64

1

1

6

36

4

16

7

49

ΣX1=20

ΣX12=60

ΣX2=54

ΣX22=378

(ΣX1)2=400

 

X2)2=2916

 

M1 = 2.50

 

M2 = 6.75

 

s1 = 1.20

 

s2 = 1.39

 

SS1 = 10.00

 

SS2 = 13.50

 

 

 

The standard error for the difference between means (sm1-m2) = ?

 

a.

0.61

 

b.

0.65

 

c.

0.92

 

d.

0.86

            Question 13

.    In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

.    X1

.    X12

.    X2

.    X22

.    1

.    1

.    7

.    49

.    3

.    9

.    7

.    49

.    3

.    9

.    9

.    81

.    2

.    4

.    5

.    25

.    4

.    16

.    5

.    25

.    2

.    4

.    8

.    64

.    1

.    1

.    6

.    36

.    4

.    16

.    7

.    49

.    ΣX1=20

.    ΣX12=60

.    ΣX2=54

.    ΣX22=378

.    (ΣX1)2=400

.     

.    X2)2=2916

.     

.    M1 = 2.50

.     

.    M2 = 6.75

.     

.    s1 = 1.20

.     

.    s2 = 1.39

.     

.    SS1 = 10.00

.     

.    SS2 = 13.50

.     

.     

.     

.    The calculated t-value = ?



. 

.    a.

. 

.    b.

. 

.    c.

. 

.    d

 

a.

-6.967

 

b.

-4.942

 

c.

-6.538

 

d.

-4.620

.    .

 

Question 14

.    What is your Step 4 decision?



. 

.    a.

.    Reject H0, t(15) = -6.967, p < .05


. 

.    b.

.    Reject H0, t(14) = -6.538, p < .05


. 

.    c.

.    Fail to Reject H0, t(6) = -4.620, p > .05


. 

.    d.

.    Fail to Reject H0, t(7) = -4.942, p > .05


15

What type of hypothesis testing error might you have made?  Explain why.

16

What is the variance value (s21) for Group 1?

 

a.

1.25

 

b.

1.12

 

c.

1.20

 

d.

1.43

17

What is the variance (s22) value for Group 2?

 

a.

1.93

 

b.

1.39

 

c.

1.30

 

d.

1.69

18

What is the calculated Fmax value?

 

a.

1.35

 

b.

0.74

19

In a study of jury behavior, two samples of participants were randomly assigned to one of two groups, with differing information concerning the evidence, about a trial in which the defendant was obviously guilty.  Both groups were presented with the evidence in a court room setting.  The first group (X1) was the control group who was presented with the evidence and given no other information, and the second group was told that some evidence had been withheld from the jury by the judge.  The first group (X1) was presented with the details at 10:00 AM in Court Room A.  The second group (X2) was presented with the same evidence at 2:00 PM in Court Room B.  The participants were asked to recommend a jail sentence, in years, which is presented in the data set below.  Test if there is a significant difference between groups with an alpha = .05, two-tailed.  Also test to see if the assumption for homogeneity of variance has been violated using an α = .05.

 

What is the Fmax critical value?

 

a.

2.86

 

b.

4.99

 

c.

3.28

 

d.

8.89

20

The assumption for homogeneity of variance was violated.

True

False

 

21

Calculate the effect size for this hypothesis test, d =

 

Is the effect size Small, Medium, or Large?

22

Write out the results in plain English including an interpretation of effect size and the 95% confidence interval.

23

.    A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

.    Subject

.    Pretest

.    Post-test

.    (X1 - X2)
D

.    D2

.    1

.    16

.    19

.    -3

.    9

.    2

.    12

.    18

.    -6

.    36

.    3

.    13

.    12

.    1

.    1

.    4

.    18

.    15

.    3

.    9

.    5

.    15

.    14

.    1

.    1

.    6

.    12

.    14

.    -2

.    4

.    7

.    12

.    17

.    -5

.    25

.     

.    ΣX1 = 98

.    ΣX2 = 109

.    ΣD = -11

.    ΣD2 = 85

.     

.    M1 = 14.00

.    M2 = 15.57

.    (ΣD)2 = 121

.     

.     

.     

.     

.    MD = -1.57

.     

.     

.     

.     

.    SS = 67.71

.     

.    
Is this a between-groups or a within-groups research design?


.    


. 

.    a.

.    between-groups


. 

.    b.

.    within-groups


.    




24

A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

Subject

Pretest

Post-test

(X1 - X2)

D

D2

1

16

19

-3

9

2

12

18

-6

36

3

13

12

1

1

4

18

15

3

9

5

15

14

1

1

6

12

14

-2

4

7

12

17

-5

25

 

ΣX1 = 98

ΣX2 = 109

ΣD = -11

ΣD2 = 85

 

M1 = 14.00

M2 = 15.57

(ΣD)2 = 121

 

 

 

 

MD = -1.57

 

 

 

 

SS = 67.71

 

 

Based on the research design you identified for this hypothesis test, what is the appropriate statistical analysis?

 

a.

one sample t-test

 

b.

t-test for independent samples

 

c.

t-test for related samples

25A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

Identify the independent variable in this study.

 

a.

Exposure to the picture of the feared object.

 

b.

The patient instructions regarding relaxation and imagery.

 

c.

Anxiety level for the pretest and post-test conditions.

 

d.

The length of time (minutes) viewing the feared object.

26

What is the measurement scale of the independent variable?

 

a.

ratio

 

b.

interval

 

c.

nominal

 

d.

ordinal

27

A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

Identify the dependent variable in this study.

 

a.

Exposure to the picture of the feared object.

 

b.

Anxiety level for the pretest and post-test conditions.

 

c.

The length of time (minutes) viewing the feared object.

 

d.

The patient instructions regarding relaxation and imagery.

28

A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

 

What is the measurement scale of the dependent variable.

 

a.

nominal

 

b.

ordinal

 

c.

interval

 

d.

ratio

29

A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

Subject

Pretest

Post-test

(X1 - X2)

D

D2

1

16

19

-3

9

2

12

18

-6

36

3

13

12

1

1

4

18

15

3

9

5

15

14

1

1

6

12

14

-2

4

7

12

17

-5

25

 

ΣX1 = 98

ΣX2 = 109

ΣD = -11

ΣD2 = 85

 

M1 = 14.00

M2 = 15.57

(ΣD)2 = 121

 

 

 

 

MD = -1.57

 

 

 

 

SS = 67.71

 

 

What is the null hypothesis (H0) for this study?

 

a.

μ1-μ< 0.00

 

b.

μD > 0.00

 

c.

μ1-μ> 0.00

 

d.

μD < 0.00

30

A technique used to help people deal with phobias is to have them counteract the feared objects used by using imagination to move themselves to a place of safety.  In an experimental test of this technique, patients sit in front of a screen and are instructed to relax.  They are then shown an image of the feared object, i.e. a picture of a spider.  The patients are instructed to signal the researcher as soon as feelings of anxiety reach a point at which viewing the image can no longer be tolerated.  The researcher records the amount of time in minutes that the patient was able to endure looking at the image.  The patient then spends two minutes imagining a “safe scene” such as a tropical beach or a familiar room before the feared object is presented again.  As before in the pre-test condition, the patient signals when the level of anxiety becomes intolerable.  Patients are expected to tolerate the feared object image longer after the imagination exercise, the post-test condition, which translates to a decrease in the phobia.  The data below summarizes the times recorded for participants.  Does the data indicate a significant increase in time viewing the feared object, and therefore a reduction in phobia using an alpha = .01, one-tailed.

Subject

Pretest

Post-test

(X1 - X2)

D

D2

1

16

19

-3

9

2

12

18

-6

36

3

13

12

1

1

4

18

15

3

9

5

15

14

1

1

6

12

14

-2

4

7

12

17

-5

25

 

ΣX1 = 98

ΣX2 = 109

ΣD = -11

ΣD2 = 85

 

M1 = 14.00

M2 = 15.57

(ΣD)2 = 121

 

 

 

 

MD = -1.57

 

 

 

 

SS = 67.71

 

 

What is the alternative hypothesis (H1) for this study?

 

a.

μD > 0.00

 

b.

μ1-μ2 < 0.00

 

c.

μD < 0.00

 

d.

μ1-μ2 > 0.00

 

Subject Mathematics
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