1. A.P. Statistics Chapter 25: Paired Samples and Blocks

2. I. Paired Data
The two groups are dependent – so we cannot use the two-sample t-methods
Focus on the difference
The sample size is the number of pairs
Mechanically, a paired t-test is just a one-sample t-test for the means of the difference

3. Assumptions and Conditions
Data must be paired
Independence condition – the groups are not independent, however, the differences must be independent of each other.
Randomized condition
10% condition
Nearly normal condition
(check using a histogram of the
differences or Normal Probability Plot)

4. Paired t -test

5. Step By Step
Read pg. 574
Did the change in schedule change the mean number of miles driven?
Confidence Intervals for Matched Pairs

6. Estimate the mean difference in age between husbands and wives.
Read page 580
Estimate the mean difference in age between husbands and wives.

7. Class Examples:
One indicator of physical fitness is resting heart rate. Ten men volunteered to test an exercise device advertised on television by using it three times a week for 20 minutes. Their resting pulse rates (beats per minute) were measured before the test began, and then again after 6 weeks. Is there evidence that this kind of exercise can reduce resting pulse rate? How much?

8. Subject Before After Difference Matt 73 Brandon 83 79 Carlos 85 81
Pulse Rates (Beats / Minute)
Subject
Before
After
Difference
Matt 73
Brandon 83 79
Carlos 85 81
David 87 86
Edwin 91
Franco 99
Graeme 84
Hans
Ivan
Jorge 76
Is there evidence that this kind of exercise can reduce resting pulse rate?
How much?