Lecture 16

# Lecture 16 - 1 Two Population Proportions Population...

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Two Population Proportions Population Parameter: p 1 p 2 The difference between two population proportions Sample Statistic: p ˆ 1 p ˆ 2 The difference between two sample proportions Remember: p ˆ = X / n where X is a binomial random variable Sampling Distribution of p ˆ 1 p ˆ 2 : Mean µ 2 1 ˆ ˆ p p - = p 1 p 2 Standard Deviation σ 2 1 ˆ ˆ p p - = ) / ( ) / ( 2 2 2 1 1 1 n q p n q p + where q = 1 – p 1

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p ˆ is called the overall proportion p ˆ = (x 1 + x 2 )/(n 1 + n 2 ) The distribution of p ˆ 1 p ˆ 2 will be approximately normal when n 1 and n 2 are large and p 1 and p 2 are not close to 0 or 1. Confidence Interval: ( p ˆ 1 p ˆ 2 ) ± z(α/2) 1 1 1 2 2 2 ˆ ˆ ˆ ˆ ( / ) ( / ) p q n p q n + 2
Example 1. A campaign manager wants to estimate the difference between men’s and women’s views regarding the candidate’s appeal. Two samples of 1000 voters are taken. 388 men favored the candidate, compared to 459 women. Find the 99% confidence interval for the difference of the proportions. 3

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4
Hypothesis Testing: H 0 : p 1 p 2 = 0

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## This note was uploaded on 02/15/2009 for the course STAT 2004 taught by Professor Melutz during the Fall '07 term at Virginia Tech.

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Lecture 16 - 1 Two Population Proportions Population...

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