10.4 Proportions

# 10.4 Proportions - Outcome 10.4 Using the sampling...

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Hypothesis Tests Statistical Inference About Means and Proportions with Two Populations BUQU 1230 Esther Tiessen Outcome 10.4— Using the sampling distribution of , be able to develop interval estimates and conduct hypothesis tests about the difference between two population proportions. p 1 - p 2

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Hypothesis Tests Two Populations Statistical inference about the difference between two population: ü means (σ1 and σ2 known) ü means (σ1 and σ2 unknown) ü means (matched samples) proportions
Hypothesis Tests Two Populations Statistical inference about the difference between two population: ü means (σ1 and σ2 known) ü means (σ1 and σ2 unknown) ü means (matched samples) proportions z -Test:Two-Sample for Proportions

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Hypothesis Tests difference between 2 population proportions: D = p 1– p 2 to make inferences about D, take independent simple random samples from 2 populations use sampling distribution of if n1 . p1 , n1 .(1 – p1 ), n2 . p2 , n2 .(1 – p2 ) are all ≥ 5, then sampling distribution of can be approximated by normal distribution mean is D = p 1– p 2 Statistical Inference about the Difference between Two Population Proportions d = p 1 - p 2 d = p 1 - p 2
Hypothesis Tests difference between 2 population proportions: D = p 1– p 2 to make inferences about D, take independent simple random samples from 2 populations use sampling distribution of if n1 . p1 , n1 .(1 – p1 ), n2 . p2 , n2 .(1 – p2 ) are all ≥ 5, then sampling distribution of can be approximated by normal distribution mean is D = p 1– p 2 Statistical Inference about the Difference between Two Population Proportions d = p 1 - p 2 d = p 1 - p 2 Use for both interval estimation and hypothesis testing

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Hypothesis Tests difference between 2 population proportions: D = p 1– p 2 sampling distribution of Statistical Inference about the Difference between Two Population Proportions d = p 1 - p 2
Hypothesis Tests Statistical Inference about the Difference between Two Population Proportions Population Proportion parameter p point estimator standard error margin of error interval estimate p σ x = p 1 - p ( 29 n z α 2 p 1 - p ( 29 n p ± z α 2 p 1 - p ( 29 n Recall from chapter 8

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Hypothesis Tests Statistical Inference about the Difference between Two Population Proportions Population Proportion Difference Between 2 Population Proportions parameter p D = p 1 – p 2 point estimator standard error margin of error interval estimate p d = p 1 - p 2 σ x = p 1 - p ( 29 n σ d = p 1 1 - p 1 ( 29 n 1 + p 2 1 - p 2 ( 29 n 2 z α 2 p 1 - p ( 29 n z α 2 p 1 1 - p 1 ( 29 n 1 + p 2 1 - p 2 ( 29 n 2 p ± z α 2 p 1 - p ( 29 n d ± z α 2 p 1 1 - p 1 ( 29 n 1 + p 2 1 - p 2 ( 29 n 2
Hypothesis Tests Statistical Inference about the Difference between Two Population Proportions Population Proportion Difference Between 2 Population Proportions parameter p D = p 1 – p 2 point estimator standard error margin of error interval estimate p d = p 1 - p 2 σ x = p 1 - p ( 29 n σ d = p 1 1 - p 1 ( 29 n 1 + p 2 1 - p 2 ( 29 n 2 z α 2 p 1 - p ( 29 n z α 2 p 1 1 - p 1 ( 29 n 1 + p 2 1 - p 2 ( 29 n 2 p ± z α 2 p 1 - p ( 29 n d ± z

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