# T-Test two samples for means

This example shows you how to perform a t-test. The t-test is used to test the null hypothesis
that the means of two populations of data are equal.

H0: μ_{1}-μ_{2} = 0

H1: μ_{1}-μ_{2} ≠ 0

First we must know if the variances of the two populations are equal or not because there are
two kinds of t-tests. In order to determine this, we have to execute an F-test.

In the following examples the variances are equal according to F-test.

The input data are:

To perform an t-test, execute the following steps:

1. Select "t-Testi" and click OK.

2. In the "Test type" box, select Equal variance.

3. In the "Test mode" box, select Two-tailed.

4. Click in the "Data1" cell range box and select the range B2:B9.

5. Click in the "Data2" cell range box and select the range C2:C7.

6. Click in the "Output" cell range box and select cell B12.

The default Alpha-value is the commonly used value 0,05. This means a 95% significance level.

7. Click OK.

### Result:

Modeller returns the p-values. If p > 0,05, we accept H0, if < 0,05, reject H0. In this case 0,0018 < 0,05,
therefore we reject the null hypothesis: the means of two manifolds are unequal at 95% significance-level.
In this example the average dissolving times of the two type coffe are unequal.