General

Two Samples Hypothesis Testing

Testing the difference between two means, independent samples.

Setting H0 and H1:

Z-test

Test statistics:

Confidence Interval, for (μ1 - μ2):

t-test

Population variances equal

Test statistics:

Where

Confidence Interval, for (μ1 - μ2):

Population variances unequal

Test statistics:

Confidence Interval, for (μ1 - μ2):

F test for equality of variances

For checking the validity of the equal variance assumption

for a two-sample t-test.

Setting H0 and H1:

Test statistics:

 assuming 

Critical value in the rejection region is based on 2 degrees of freedom, each n - 1

So, 

t test for comparing two means for dependent samples or paired samples.

Setting H0 and H1:

Test statistics:

Where

 and

Confidence Interval, for μd:

ANOVA Test

ANalysis-Of-VAriance table could test the Difference among three or more means.

Setting H0 and H1:

H0: all populations means are equal.

H1: at least one μ differs.

Variation	DF	Sum of Squares	Mean Square	F
Treatment
Error
Total

N is overall sample size.

k is the number of groups.