1. Large sample test
for a difference between
two proportions

3. Conditions
• Simple random Sample
• Samples are Independent
• Each sample point has just two possible
outcomes (success and failure)
• Sample includes at least 10 successes and 10
failures
(np>10 and nq>10 )
• Population size is at least 10 times larger than
the sample

4. 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: P1=P2 & Ha: P1 = P2
2- Analysis Plan
* Test Method: use a 2 proportion z-test to determine
whether the hypothesized differenced between the
population proportions differs significantly from the observed
sample difference

5. 3- Analyze: find the TS and its associated P-value
** Standard Error:
**Pooled sample Proportion: (when P1=P2) then…
**both of these can be found in the table under two-sample
*P-value- probability of observing a sample statistic as extreme
as the TS (where the TS is a z-score) (Use Appendix A )
4- Interpret- compare the P-value to the significance level and reject
null when the P-value is less than the Significance level