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If I poll 10 people (with a yes/no question), and all of them respond with 'yes', should I report the rate of 'no' answers (in the greater population) is "zero plus or minus zero", or simply be confident that it is "less than one in five"?

I ask because using the "margin of error" (or "standard error of the proportion") formula sqrt[p(1-p)/n] it would appear, counter-intuitively, that the confidence interval narrows to zero (regardless of how few the samples) when the sample proportion is 0 or 1.

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# Margin of error, if all responses identical

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