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I saw the following statistic on TV a few years back:

53% of voters are going to vote for Mitt Romney over Barack Obama (Error: 3%, sample size: 300, survey conducted via phone)

After seeing this, I wrote the following in my notes:

Let's say that a politician is polling at a 53% rating, and the "error" (Standard Error) is 3%. Does this mean that the politician is actually polling between 50% and 56%? No. It actually means that 95% of the votes are between 47% and 59% (because a +- 2 standard deviation span contains 95% of incidents), and actually only 67% of the votes are between 50% and 56% (because a +- 1 standard deviation span contains 67% of incidents)

Questions:

  1. Did I interpret it correctly? If not then what is the correct (or a better) interpretation?

  2. I understand how Standard Error is calculated in a Linear Regression. But how is the Error calculated in a situation like this where one is simply asking 300 people whether they're going to vote for A or B?

(please feel free to improve my tags.)

thanks_in_advance
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    This question [has been answered](http://stats.stackexchange.com/q/16413/28500) elsewhere on this site. Note that in the case you present (300 cases, 3% error), the claimed error is the standard error of the estimate. See [this Wikipedia page](https://en.m.wikipedia.org/wiki/Margin_of_error) for further background. – EdM Jan 30 '16 at 01:10
  • @EdM I disagree that this is a ***duplicate*** of that question. There are similarities, but there are also differences. It would be better if this answer could be answered independently. – thanks_in_advance Feb 01 '16 at 01:43
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    As the note from @whuber on duplication suggests, the best way to get an independent answer would be to pose a new question that clearly indicates the specific issues that haven't been addressed in the answer to the linked previous question. – EdM Feb 01 '16 at 02:15

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