Confidence Intervalfor a difference between

two Paired Means

Paired Data• Two data sets are paired when there is a 1-1 relationship between

the values in the two data sets, meaning…– Each data set has the same number of data points – Each data point in one data set is related to one and only one

data point in the other data set

– Must use a matched pairs t-test to see if there is a significant difference in the means from paired data.

EX: Matching the times of a group of runners sprinting a mile at the start of their training, and then a month after their training.

CI for a difference between Paired Means Estimation Requirements1. The data set is a Simple random sample of observations from the population

of interest2. Each element of the population includes data on two paired variables, such

that the paired difference between them is: d= a-b3. Sampling distribution of mean difference between the data pairs (d) is

approximately normally distributed4. Data sets are not independent

How to find the CI for the mean difference with Paired Data5. Sample statistic (use mean difference between sample data pairs, d, to

estimate the mean difference between population data pairs, μd)6. Confidence Level7. Margin of error: use t-score where the DF= n-18. Specify the CI- sample statistic + ME

written as: (Sample Stat – ME, Sample Stat + ME)

Variability of the Mean differencebetween Matched Pairs

• If d is the mean difference between sample data pairs, we need to compute the SE of the sampling distribution for d.

• When the population is at least 10 times larger than the sample size, SE can be approximated: