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Chapter 12: Inference for Proportions BY: Lindsey Van Cleave

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12.1: Inference For a Population Proportion The statistic that estimates the parameter p is the sample proportion:

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12.1: Inference For a Population Proportion p is an unbiased estimator of the population proportion…

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12.1: Inference For a Population Proportion The distribution of p can be assumed to be normal if… 1. The population is at least 10 times the sample. 2. np is at least n(1-p) is at least 10 Is p is found to be normal use the following formula to standardize it

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12.1: Inference For a Population Proportion To test the null hypothesis H 0 : p=p 0 that the unknown p has a specific value, p 0, just replace p by p 0 in the z statistic and in checking the values of np and n(1-p).

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12.1: Inference For a Population Proportion In a confidence interval for p, we have no specific value to substitute. In large samples, p, will be close to p. So we replace p by p in determining the values of np and n(1-p). We also replace the standard deviation by the standard errror of p

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12.1: Inference For a Population Proportion To determine the sample size n that will yield a level C confidence interval for a population proportion p with a specified margin of error m:

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Comparing Two Proportions In a two-sample problem we want to compare two populations or the responses to two treatments based on two independent samples. We compare the population by doing inference about the difference p 1 -p 2

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Comparing Two Proportions Standard Deviation: Confidence Interval

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Comparing Two Proportions Dont worry you can do all of the significance tests in your calculator: 1. STAT and then TESTS #6: 2-PropZTest Enter info and push calculate Then there is your correct response!

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