Hypothesis Tests for Difference Between

Paired Means

Conditions

• Simple random Sample• The samples are not independent (based on

paired data) • The sampling distribution is approximately

normally distributed

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 2μ > d μ < d 1μ < 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

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