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Chapter 19

# Chapter 19 - Chapter 19 Confidence Intervals for...

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Chapter 19 Confidence Intervals for Proportions

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Review Recall the sampling distribution for sample proportions (under certain conditions that we will be careful to check): n pq p N ,
Review The conditions we need to check are: 1. 10% Condition – the sample size, n , should be less than 10% of the population size 2. Success/Failure – np>10, nq>10

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Review p is the proportion of interest from the population. We calculate from our sample. We can make inferences about our population from our estimate. p ˆ
Review/Standard Error 68-95-99.7 Rule In order to create a diagram we need the center and the standard deviations. Use estimates to come up with sample proportion and sample standard deviation. We call sample standard deviation: STANDARD ERROR ) ˆ ( ˆ ˆ ˆ p SE n q p n pq p = = σ

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What does this tell us? n q p p n q p p n q p p p n q p p n q p p n q p p ˆ ˆ 3 ˆ ˆ 2 ˆ ˆ ˆ ˆ ˆ ˆ 2 ˆ ˆ 3 + + + - - - n q p p n q p p n q p p p n q p p n q p p n q p p ˆ ˆ 3 ˆ ˆ ˆ 2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 2 ˆ ˆ ˆ 3 ˆ + + + - - -
What does this tell us? Let’s think about the second interval (95%). Start with (because we know this value) and go out about 2 in either direction. We can be 95% sure (confident) that p will be in that interval. The numbers at the 95% place markers are the endpoints of an important statistical tool. CONFIDENCE INTERVAL p ˆ ) ˆ ( p SE

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Election 2004 You have seen Confidence Intervals before! Oct. 9-10 CNN/USA Today/Gallup Poll (793 likely voters) Kerry 49% President Bush 48% Margin of Error: ± 3%
War on Terrorism According to the Feb. 8 CNN/USA Today/Gallup poll of 1,010 adult Americans, 35% of those surveyed were dissatisfied with the way the war on terrorism was going. This poll was conducted by Gallup, a national polling organization, so we can assume that the conditions check out.

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War on Terrorism Let’s talk about the sampling distribution of the sample proportion of adults who are dissatisfied with the way the war on terrorism is going. What do we know? n = 1,010 = .35 p ˆ
War on Terrorism 045 . 0 03 . 0 015 . 0 015 . 0 03 . 0 045 . 0 + + + - - - p p p p p p p

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War on Terrorism About 95% of the time (i.e. for about 95% of random samples), will be no more than 0.03 away from p Start at = 0.35 and go out about 0.03 in each direction We can be 95% confident that p is in this interval; i.e., we can be 95% confident that the true proportion of adults who are dissatisfied with the way the war on terrorism is going is between 32% and 38%.
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Chapter 19 - Chapter 19 Confidence Intervals for...

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