document.write( "Question 1119653: A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 14% chose chocolate pie, and the margin of error was given as +/-3 percentage points. Describe what is meant by the statement that \"the margin of error was given as +/- 3 percentage points.\" \n" ); document.write( "

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It means that we are highly confident (probably 95%) that the true value of the entire population (which we can never know) is likely (highly confident) between 11 and 17%. What isn't said is that any value in that interval is equally likely, but the 14% was the point estimate, meaning that was the value for those 2000 people.. \r
\n" ); document.write( "\n" ); document.write( "Also what is of concern is that \"2000 respondents\" suggests some lack of randomization. \r
\n" ); document.write( "\n" ); document.write( "Another way of saying it is that we could take multiple polls of 2000 from the same population (different people) and 95% of them (typical value) would have results somewhere in the 11-17% interval. We just don't know which ones are right. \r
\n" ); document.write( "\n" ); document.write( "note that the true value either is or isn't in the interval (100/0). Because that is not a useful probability statement, we use confidence. \n" ); document.write( "

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