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Perform a three way t-test on the following data: 5.31 +/- 2.32 (n=3), 1.89 +/- 0.368...

Perform a three way t-test on the following data: 5.31 +/- 2.32 (n=3), 1.89 +/- 0.368 (n=3), and 8.08 +/- 0.0495 (n=2).

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Expert Solution

Perform a three way t-test on the following data: 5.31 +/- 2.32 (n=3), 1.89 +/- 0.368 (n=3), and 8.08 +/- 0.0495 (n=2).

Comparison of 1 and 2

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

3

Sample Mean

5.31

Sample Standard Deviation

2.32

Population 2 Sample

Sample Size

3

Sample Mean

1.89

Sample Standard Deviation

0.368

Intermediate Calculations

Population 1 Sample Degrees of Freedom

2

Population 2 Sample Degrees of Freedom

2

Total Degrees of Freedom

4

Pooled Variance

2.7589

Standard Error

1.3562

Difference in Sample Means

3.4200

t Test Statistic

2.5218

Two-Tail Test

Lower Critical Value

-2.7764

Upper Critical Value

2.7764

p-Value

0.0652

Do not reject the null hypothesis

Comparison of 1 and 3

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

3

Sample Mean

5.31

Sample Standard Deviation

2.32

Population3 Sample

Sample Size

2

Sample Mean

8.08

Sample Standard Deviation

0.0495

Intermediate Calculations

Population 1 Sample Degrees of Freedom

2

Population 3 Sample Degrees of Freedom

1

Total Degrees of Freedom

3

Pooled Variance

3.5891

Standard Error

1.7294

Difference in Sample Means

-2.7700

t Test Statistic

-1.6017

Two-Tail Test

Lower Critical Value

-3.1824

Upper Critical Value

3.1824

p-Value

0.2075

Do not reject the null hypothesis

Comparison of 2 and 3

Pooled-Variance t Test for the Difference Between Two Means

(assumes equal population variances)

Data

Hypothesized Difference

0

Level of Significance

0.05

Population 2 Sample

Sample Size

3

Sample Mean

1.89

Sample Standard Deviation

0.368

Population 3 Sample

Sample Size

2

Sample Mean

8.08

Sample Standard Deviation

0.0495

Intermediate Calculations

Population 2 Sample Degrees of Freedom

2

Population 3 Sample Degrees of Freedom

1

Total Degrees of Freedom

3

Pooled Variance

0.0911

Standard Error

0.2755

Difference in Sample Means

-6.1900

t Test Statistic

-22.4659

Two-Tail Test

Lower Critical Value

-3.1824

Upper Critical Value

3.1824

p-Value

0.0002

Reject the null hypothesis


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