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B.5 diff between proportions

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B.5 diff between proportions

1. 1. Large sample test for a difference between two proportions
2. 2. 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
3. 3. 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
4. 4. 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