run an independent ttest Does the result reach significance

run an independent t-test. Does the result reach significance?

set 1:

8, 6, 2, 8, 6, 7, 3, 6, 6, 5, 7, 4, 6, 7, 5, 3, 4, 5, 9, 1

set 2:

9, 6, 2, 8, 7, 7, 5, 7, 5, 7, 7, 6, 7, 8, 7, 4, 6, 5, 9, 7

Solution

run an independent t-test. Does the result reach significance.

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

20

Sample Mean

5.4

Sample Standard Deviation

2.0876

Population 2 Sample

Sample Size

20

Sample Mean

6.45

Sample Standard Deviation

1.6694

Intermediate Calculations

Population 1 Sample Degrees of Freedom

19

Population 2 Sample Degrees of Freedom

19

Total Degrees of Freedom

38

Pooled Variance

3.5724

Standard Error

0.5977

Difference in Sample Means

-1.0500

t Test Statistic

-1.7568

Two-Tail Test

Lower Critical Value

-2.0244

Upper Critical Value

2.0244

p-Value

0.0870

Do not reject the null hypothesis

At 5% level, calculated t = -1.7568, P=0.087 is not significant.

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	20
Sample Mean	5.4
Sample Standard Deviation	2.0876
Population 2 Sample
Sample Size	20
Sample Mean	6.45
Sample Standard Deviation	1.6694
Intermediate Calculations
Population 1 Sample Degrees of Freedom	19
Population 2 Sample Degrees of Freedom	19
Total Degrees of Freedom	38
Pooled Variance	3.5724
Standard Error	0.5977
Difference in Sample Means	-1.0500
t Test Statistic	-1.7568
Two-Tail Test
Lower Critical Value	-2.0244
Upper Critical Value	2.0244
p-Value	0.0870
Do not reject the null hypothesis