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).

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

milcah answered 4 months ago

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