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.

For more information about Hypothesis Test for Paired Observations click here.



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 < \( \alpha \) )


Running a two paired sample T test


Do it yourself

Step 1: Go to "Attachments" on the bottom of this page and dowload the Excel spreadsheet.

Step 2: Follow the steps teached in the video above and solve the exercises in the Excel spredsheet dowloaded. 

Step 3: Answer the questions in the Interactive Content below.