1. Paired Samples and Blocks
Chapter 25
Paired Samples and Blocks

2. Topics
Knowing when and how to use the paired t-test for means

3. What if our data are not independent?
If our data is not independent, the two-sample t-test from Chapter 24 may not be applicable.
Look for paired data.

4. Example
A pizza delivery company underwent a management change at the end of The recipes were changed, the cars were updated, and the drivers underwent an intensive training course. Did the change have a positive affect on sales from 2002 to 2003?

5. Sales Data

6. Pizza Sales ctd.
Why does a two-sample t-test not make sense here?

7. Pizza Sales ctd.
We are really going to test to see if there is a difference between the paired data.
i.e. Is there a difference in the month to month sales from 2002 to 2003.
In paired data, Independence means the individual differences must be different. In this problem, that means the difference in pizza sales from August are unlikely to affect the difference in pizza sales from November.

8. Performing a Paired t-test
A Paired t-test is really a one-sample t-test on the differences.
Step 1: Find the differences.
Step 2: Find the sample mean and standard deviation.
Step 3: State your hypotheses:

9. Example ctd.
Perform the hypothesis test:
Results: