SOLUTION: 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
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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." Found 2 solutions by Boreal, solver91311:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! 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..
Also what is of concern is that "2000 respondents" suggests some lack of randomization.
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.
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.
For a confidence interval of , a population proportion with a margin of error of means that the true population proportion will be in the range of the time.
In other words, the magazine statistic is meaningless because no confidence interval was specified. The magazine statement could very well be true for a confidence interval of, say, 5%, which says the statistic is valid 5% of the time and complete nonsense 95% of the time. Or any other value for the confidence interval. Of course, any professional statistician who published a margin of error based on such a broad confidence interval should spend a day in the stocks in the town square the target of jeers and rotten vegetables.
John
My calculator said it, I believe it, that settles it
