# Margin of Error

Suppose you are a pollster for a major political organization and you want to say with 99.9% certainty that the majority of the country disapproves of the current administration, but that you don't have very much time.

So you conduct a study with $$50$$ respondents. $$35$$ of them say they do not approve. This seems like great news, that $$70\%$$ of the sample does not approve. Even if these $$50$$ are a truly random sample of the population, what's your sampling error rate? What's your margin of error on a $$99.9\%$$ confidence interval?

Express your answer as a decimal. For instance, $$10\%$$ would be $$0.1.$$

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