Statistics Homework

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1.       When should you use a factorial ANOVA rather than a simple ANOVA to test the significance of the difference between the average of two or more groups?

 

2.       Create a drawing or plan for a 2 x3 experimental design that would lend itself to a factorial ANOVA.  Be sure to identify the independent and dependent variables.

 

3.       #4 Use Chapter 14 Data set 3 (below) and answer the following questions in an analysis of whether level of stress and gender has an impact on caffeine consumption (measured as cups of coffee per day).

 

a.       Is there as difference between the levels of caffeine consumption for the high-stress, low-stress, and no-stress groups?

 

b.      Is there a difference between males and females, regardless of stress group?

 

c.       Any interactions?

 

Chapter 14 Data set 3

 

severeity

treatment

Pain Score

severity

Treatment

Pain Score

1

Drug #2

5

2

Placebo

5

1

Drug #2

4

2

Placebo

6

1

Drug #2

5

2

Placebo

5

1

Drug #2

4

2

Placebo

4

1

Drug #2

3

2

Placebo

4

1

Drug #2

3

2

Placebo

6

1

Drug #2

3

2

Placebo

5

1

Drug #2

4

2

Placebo

4

1

Drug #2

5

2

Placebo

2

1

Drug #2

5

2

Placebo

1

1

Drug #2

5

2

Placebo

3

1

Drug #2

6

2

Placebo

2

1

Drug #2

6

2

Placebo

2

1

Drug #2

7

2

Placebo

3

1

Drug #2

6

2

Placebo

4

1

Drug #2

5

2

Placebo

3

1

Drug #2

7

2

Placebo

2

1

Drug #2

6

2

Placebo

2

1

Drug #2

8

2

Placebo

1

Gender

Caff_Consumption

Stress

1

5

1

1

6

3

2

7

3

1

7

2

1

5

3

1

6

 

1

8

2

1

8

2

2

9

1

2

8

1

2

9

1

2

7

2

2

4

1

2

3

1

1

0

1

2

4

2

1

5

1

2

6

2

1

2

2

1

4

3

1

5

3

2

5

3

1

4

2

1

3

2

1

7

3

2

8

2

1

8

2

1

11

1

1

2

2

1

3

1

  

 

   

 

   

 

   

 

   

 

         

 

 

 

 

 

1.       Given the following information, Use Table B.4 in Appendix B to determine whether the correlations are significant and how you would interpret the results.

 

a.       The correlation between speed and strength for 20 women is 567.  Test these results at the .01 level using a one-tailed test.

 

b.      The correlation between the number correct on a math test and the time it takes to complete the test is -.45.  Test where the correlation is significant for 80 children at the .05 level of significance.

 

Choose either a one –or a two –tailed test and justify your choice.

 

c.       The correlation between number of friends and grade point average (GPA) for 50 adolescents is 37. Is this significant at the .05 level for a two-tailed test?

 

One Tailed Test(  DF)

0.05

0.01

Two-Tailed (df)

0.05

0.01

 

1

0.9877

0.9995

1

0.9969

0.9999

 

2

0.9

9800

2

0.95

9900

 

3

0.8054

0.9343

3

0.8783

0.9587

 

4

0.7293

0.8822

4

0.8114

0.9172

 

5

0.6694

0.832

5

0.7545

0.8745

 

6

0.6215

0.78887

6

0.7067

0.8343

 

7

0.5822

0.7498

7

0.6664

0.7977

 

8

0.5494

0.7155

8

0.6319

0.7646

 

9

0.5214

0.6851

9

0.021

0.7348

 

10

0.4973

0.6581

10

0.576

0.7079

 

11

0.4762

0.6339

11

0.5529

0.6835

 

12

0.4575

0.612

12

0.5324

0.6614

 

13

0.4409

0.5923

13

0.5339

0.6411

 

14

0.4259

0.5742

14

0.4973

0.6226

 

15

0.412

0.5577

15

0.4821

0.6055

 

16

4000

0.5425

16

0.4683

0.5897

 

17

0.3887

0.5285

17

0.4555

0.5751

 

18

0.3783

0.5155

18

0.4438

0.5614

 

19

0.3687

0.5034

19

0.4329

0.5487

 

20

0.3598

0.4921

20

0.4227

0.5368

 

25

0.3233

0.4451

25

0.3809

0.4869

 

30

0.296

0.4093

30

0.3494

0.4487

 

35

0.2746

0.381

35

0.3246

0.4182

 

40

0.2573

0.3578

40

0.3044

0.3932

 

45

0.2428

0.3384

45

0.2875

0.3721

 

50

0.2306

0.3218

50

0.2732

0.3541

 

60

0.2108

0.2948

60

0.25

0.3248

 

70

0.1954

0.2737

70

0.2319

0.3017

 

80

0.1829

0.2565

80

0.2172

0.283

 

90

0.1726

0.2422

90

0.205

0.2673

 

100

0.1638

0.2301

100

0.1946

0.254

 

 

4.       (Use Data Set info from above again) Answer the following questions below.  Compute the correlation coefficient manually .

 

A.      Test for the significance of the correlation coefficient at the .05 level using a two-tailed test between hours of studying and grade.

 

B.      Interpret the correlation.  What do you conclude about the relationship between the number of hours spent studying and the grade received on a test?

 

C.      How much variance is shared between the two variables?

 

D.      How do you interpret the results?

 

5.       A study was completed that examined the relationship between coffee consumption and the level of stress for a group of 50 undergraduates.  The correlation was .373, and it was a two-tailed test, done at the .01 level of significance.  First, is the correlation significant? Second, what’s wrong with the following statement? “As a result of the data collected in this study and out rigorous analyses, we have concluded that if you drink less coffee, you will experience less stress.”

 

6.       Use the following set of data to answer the questions, Do this one manually.

 

Age in Months

Number of Words known

12

6

15

8

9

4

7

5

18

14

24

18

15

7

16

6

21

12

15

17

 

A.      Compute the correlation between age in months and number of words known.

 

B.      Test for the significance of the correlation at the .05 level of significance.

 

C.      Recall what was learned about correlation and coeffecients and interpret this correlation.

 

 

 

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