## 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.