In: Math
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).
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 |