B.5 diff between proportions
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This document describes how to conduct a large sample test for the difference between two proportions. It outlines the conditions needed, including independent simple random samples of at least 10 successes and failures from populations at least 10 times the sample size. It then explains the steps to conduct the test: 1) state the null and alternative hypotheses, 2) use a two proportion z-test as the analysis plan, 3) analyze to find the test statistic and p-value, and 4) interpret by comparing the p-value to the significance level.
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B.5 diff between proportions
- 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