# StatisticsExcel_HypothesisTestForPairedObservations

Hypothesis Test for Paired Observations:

• When to use it: to test two sample means when their respective population variances are unknown but considered equal and with data recorded in pairs.

## Example

Verify if the 103 dimensional characteristic was modified by a thermal treatment by applying a 95% TH for $\mu_d = \mu_1 - \mu_2$ (n=10)

Before TT After TT
47.39 47.28
47.47 47.33
47.58 47.46
47.60 47.47
47.40 47.28
47.68 47.58
47.47 47.36
47.64 47.54
47.48 47.37
47.73 47.61

## Using Excel

Select Data, Data Analysis, t-test: Paired two-sample for means

Excel should calculate the following:

For a two-sided test, the null hypothesis is rejected (p-value = 3.36E-10 < $\alpha$ )