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# Comparing Two Proportions - AP Stats Chapter 22

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Tweet## Steve Mays

on 8 February 2013#### Transcript of Comparing Two Proportions - AP Stats Chapter 22

Comparing Two Proportions AP Stats - Chapter 22 There are many similarities between inference for proportions and inference when comparing proportions. To begin with we will still be using a Normal model to make our inference and if that's the case, we will need a way to find the STANDARD DEVIATION of the DIFFERENCE BETWEEN TWO PROPORTIONS. The formula for the standard deviation of the difference between two proportions is . . . Standard Deviation vs Standard Error At this point I want to explain the difference between standard deviation of a sampling distribution and the standard error. Assumptions and Conditions The following are the A/C for the difference between proportions . . . Randomization Condition The 10% Condition Independent Groups Assumption Success/Failure Condition Once again we need our sample to be randomly chosen, so that it represents the population. The sample size of the groups, should not be more than 10% of the population. We must make sure that our GROUPS are independent of one another. If they are not independent, then we cannot even, "proceed with caution". If they were DEPENDENT, then that's another test entirely. Both groups need to have at least 10 successes and 10 failures. A Two-Proportion Z-Interval Hypothesis Tests for the Difference Between Proportions Before we get to an example, you need to know that we use a "pooled" standard deviation for our test statistic. See below how the p-hat and q-hat are "pooled". The reason for this is because we are assuming that the null hypothesis is true. And the null hypothesis for testing the difference between proportions says that there is NO DIFFERENCE between the two proportions. And since we are assuming that there is no difference, we can throw our sample data from both groups into the same "pool". Here's the formula to find the pooled p-hat. Now to an example of a hypothesis test for the difference between proportions. Just for fun . . . See you in stats class!

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