1. Hypothesis test for
Difference Between
Means (unpaired)

2. •

3. •

5. Conditions
• Simple random Sample
• The samples are independent
• Each population is at least 10 times larger
than each sample size
• The sampling distribution is approximately
normally distributed

6. Conducting a Hypothesis test
1- state the hypothesis: Ho & Ha (mutually exclusive)
*when the null hypothesis states there is no difference between
the 2 population proportions (d=0), and it is a two tail test, then :
Ho: μ1= μ2 & Ha: μ 1 = μ2
2- Analysis Plan
* Test Method: use a 2 sample t- test to determine whether
the hypothesized difference between the population means differs
significantly from the observed sample difference

7. 3- Analyze: find the TS and its associated P-value for a t-test
SE: s1= SD of sample 1
s2= SD of sample 2
n1= sample size of sample 1
n2= sample size of sample 2
**DF would be smaller of: n1-1 or n2-1
*TS: t = (x1-x2) x1= mean of sample 1
SE x2= mean of sample 2
*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