Lecture_26,_Chap_11,_Sec_3New

Lecture_26,_Chap_11,_Sec_3New - Chapter 11 Section 3...

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Chapter 11 Section 3 Inference about Two Population Proportions

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Two Population Proportions Learning objectives Test claims regarding two population proportions Construct and interpret confidence intervals for the difference between two population proportions Determine the sample size necessary for estimating the difference between two population proportions within a specified margin of error 2 1 3
Two Population Proportions This progression should not be a surprise Chapter 9 – confidence intervals for one mean, one proportion, one standard deviation Chapter 10 – hypothesis tests for one mean and one proportion Chapter 11 – hypothesis tests for two means, two proportions, (guess what’s after this …)

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Two Population Proportions We now compare two proportions, testing whether they are the same or not Examples The proportion of women (population one) who have a certain trait versus the proportion of men (population two) who have that same trait The proportion of white sheep (population one) who have a certain characteristic versus the proportion of black sheep (population two) who have that same characteristic
Two Population Proportions The test of two populations proportions is very similar, in process, to the test of one population proportion and the test of two population means The only major difference is that a different test statistic is used

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Two Population Proportions 1 1 1 n / x p ˆ = 2 2 2 n / x p ˆ = In the test of two proportions, we have two values for each variable – one for each of the two samples 2 1 p ˆ p ˆ -
Two Population Proportions For the test of two proportions, to measure the deviation from the null hypothesis, it is logical to take which has a standard deviation of 2 2 2 1 1 1 1 1 n ) p ( p n ) p ( p - + - ) p p ( ) p ˆ p ˆ ( 2 1 2 1 - - -

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Two Population Proportions Thus for the test of two proportions, under certain appropriate conditions, the difference is approximately normal with mean 0, and the test statistic has an approximate standard normal distribution 2 2 2 1 1 1 2 1 2 1 1 1 n ) p ( p n ) p ( p ) p p ( ) p ˆ p ˆ ( z - + - - - - = ) p p ( ) p ˆ p ˆ ( 2 1 2 1 - - -
Two Population Proportions Now for the overall structure of the test 1. Set up the hypotheses 2. Select the level of significance α 3. Compute the test statistic 4. Compare the test statistic with the appropriate

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This note was uploaded on 08/04/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

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Lecture_26,_Chap_11,_Sec_3New - Chapter 11 Section 3...

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