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Standard Deviations Sample Sizes Assume Equal Standard Deviations (Pooled) Do Not Assume Equal Standard Deviations (Not Pooled) Study T test statistic Degrees of Freedom P-value

Standard Deviations

Sample Sizes

Assume Equal Standard Deviations (Pooled)

Do Not Assume Equal Standard Deviations (Not Pooled)

Study

T test statistic

Degrees of Freedom

P-value

T test statistic

Degrees of Freedom

P-value

1

12

10

20

20

1.431

38

0.1605

1.431

36.80

0.1607

2

12

10

50

50

2.263

98

0.0258

2.263

94.91

0.0259

3

6

5

20

20

2.863

38

0.0068

2.863

36.80

0.0069

4

6

6

32

8

2.108

38

0.0417

2.108

10.79

0.0593

5

8

6

20

20

2.236

38

0.0313

2.236

35.24

0.0318

6

8

6

10

30

2.097

38

0.0427

1.814

12.55

0.0937

7

8

6

30

10

1.808

38

0.0785

2.088

20.58

0.0494

8

12

2

20

20

1.838

38

0.0739

1.838

20.05

0.0809

9

12

2

10

30

2.246

38

0.0306

1.312

9.17

0.2216

10

12

2

30

10

1.301

38

0.2012

2.193

33.29

0.0354

What do we learn from this? Answer the following questions.

  1. Compare Studies 5 - 10: In which two of these studies does the assumption regarding the equality of the population standard deviations have the least effect on the two p-values?

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