This document outlines the steps for conducting a hypothesis test comparing the means of paired data. It explains that the test assumes a simple random sample of paired data that is approximately normally distributed. The steps include stating the null and alternative hypotheses about the difference between population means, using a paired t-test method to test the sample data, and interpreting the results by comparing the p-value to the significance level.

1. Hypothesis Tests for
Difference Between
Paired Means

2. Conditions
• Simple random Sample
• The samples are not independent (based on
paired data)
• The sampling distribution is approximately
normally distributed

3. Conducting a Hypothesis test
1- state the hypothesis: Ho & Ha (mutually exclusive)
d= difference between paired values from two data sets
d= x1-x2 (where x1 and x2 are sample means for the two data
sets)
Null Hypothesis Alternative Hypothesis # of Tails
μ = d μ = d 2
μ > d μ < d 1
μ < d μ > d 1
2- Analysis Plan
* Test Method: use a matched pairs t-test to determine whether the
difference between sample means for paired data is significantly different from
the hypothesized difference between population means

4. 3. Analyze Sample Data - Using sample data, test statistic, and the P-
value associated with the test statistic.
* SE= s/ √n
* TS: t= (x- D) where x= sample mean of differences and
SE
*P-value- probability of observing a sample statistic as extreme as the
TS (where the TS is a t-score)
4- Interpret- compare the P-value to the significance level and reject
null when the P-value is less than the Significance level