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Question 278:

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The calculations for an exact confidence interval are rather complicated. You can find references to some equations in this paper. You can also see a formula in excel using this spreadsheet available in the Restoring Confidence in Usability Results page, where there are more references. 

The fastest way to compute an exact confidence interval is to use the confidence interval around a proportion calculator, enter 167/300 and select 99% as the confidence level. You should get a 99% exact CI of ~(48% to 63%).

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