1. AP Statistics Chapter 25 Notes
“Matched Pairs Testing”

2. Matched Pairs
Looks like a 2 sample mean test but the groups ARE NOT INDEPENDENT, they are matched pairs.
Example:
A group of students take a pretest and a posttest and we compare the mean scores to see if the scores on the posttest show improvement

3. A Paired T-test
STAT, TESTS #2 L3
STAT, TESTS #8 L3
Use the formulas for the one-sample t-test but you are analyzing the differences in your means like for the two-sample t-test. (Use L3 as the difference of L1 and L2)
Ho: d = 0 Ha: d < 0, d > 0, d = 0
SE =

4. Example
In many countries husbands tend to be slightly older than their wives. The given data has been taken from a random sample of 16 British couples to estimate the mean difference of husband’s and wife’s ages among British couples. Is this sufficient evidence that husbands in Britain are on average older than their wives? If so, how much older?
Wife’s Age 43 28 30 57 52 27 23 25 39 32 35 33
Husband’s Age 49 40 58 47 31 26 38

5. The Solution Process
This is a matched pairs t-test, not a 2-sample t-test because the groups are not independent. We are looking for a confidence interval for the mean difference in the husband’s and the wife’s ages.
Enter the data into L1 and L2, then set up L3 to be the difference of L1 and L2
1. State the hypotheses.
2. Check the conditions.
Random sample – given information
Matched pairs - the data is a set of matched pairs
The population of all married couples in Great Britain must be at least 160 couples
Check a histogram of L3 -

6. The Solution Process
3. Perform the significance test in Stat, Tests, #2.
4. State your conclusion.
Find the confidence interval in Stat, Tests, #8.
How much older are the husbands?