UT Knoxville STAT 201 - Chapter 19 (38 pages)
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Chapter 19
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- Pages:
- 38
- School:
- University of Tennessee
- Course:
- Stat 201 - Introduction to Statistics
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Unformatted text preview:
Chapter 19 Chapter19 Presentation 1213 Confidence Intervals for Proportions Copyright 2009 Pearson Education Inc 1 The Margin of Error When asked When you see or hear about an athlete breaking a world record in Swimming are you suspicious that the athlete used performance enhancing drugs 24 of 1007 US adults surveyed responded yes with a margin or error of 3 percentage points What does a margin of error mean what does it tell us and where does it come from Chapter19 Presentation 1213 Copyright 2009 Pearson Education Inc 2 The Margin of Error Cont Polling agencies have agreed what to report as the Margin of Error If the poll like the one on the previous slide is designed to estimate a population proportion the Margin of Error is approximately two times SD p Chapter19 Presentation 1213 Copyright 2009 Pearson Education Inc pq n 3 But what if we don t know p The formula on the previous slide is the standard deviation of the sampling distribution of the sample proportion you learned in Chapter 18 That formula involves the population proportion p Usually p is what we d like to know and why we took a sample to begin with Chapter19 Presentation 1213 Copyright 2009 Pearson Education Inc 4 But what if we don t know p Cont If we don t know p we re stuck right Not really We will use our sample statistic estimate the population parameter p in that formula to Whenever we estimate the standard deviation of a sampling distribution we call it a standard error Chapter19 Presentation 1213 Copyright 2009 Pearson Education Inc 5 Standard Error For a sample proportion the standard error is SE p pq n We can use SE p in place of SD p as an estimate when describing the sampling distribution Chapter19 Presentation 1213 Copyright 2009 Pearson Education Inc 6 Analyzing the World Record Swimmers Poll 24 responded they were suspicious of performance enhancing drug use among swimmers who break world records Is the proportion of all US adults who are suspicious close to 24 Probably But how close
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