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Confidence Interval of a Survey

Tool for measuring the upper and lower bounds of the confidence interval attributable to a survey. The 95% or 99% confidence interval makes it possible to better qualify the quality of a survey.

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Confidence Interval of a Survey -

Tag(s) : Statistics

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Confidence Interval of a Survey

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Tool for measuring the upper and lower bounds of the confidence interval attributable to a survey. The 95% or 99% confidence interval makes it possible to better qualify the quality of a survey.

Answers to Questions

What is a confidence interval? (Definition)

Definition: A confidence interval is a lower and upper bound that defines a margin of error for the raw results of a survey. The confidence interval evaluates the quality and accuracy of the estimate obtained with the sample surveyed.

How to calculate a confidence interval?

For a survey of \( N \) people resulting in the probability \( p \), then the 95% confidence interval is $$ \left[p-1.96\frac{\sqrt{p(1-p)}}{\sqrt n},p+1.96\frac{\sqrt{p(1-p)}}{\sqrt n}\right] $$

With 1.96 the value of the 2.5 percentile of the normal distribution.

Example: For a poll with a sample of 80 people of whom 60 will vote YES, the probability \( p = 60/80 = 0.75 \), the confidence interval is \( \left[0.75-1.96\frac{\sqrt{0.75(1-0.75)}}{\sqrt 80},0.75+1.96\frac{\sqrt{0.75(1-0.75)}}{\sqrt 80}\right] = \left[ , \right] \). This means that there is 95% chance in the final vote the YES result is between 65.5% and 84.5%.

What is the rule of three?

When the probability is close to 0, the calculation of the confidence interval can lead to probabilities outside the interval \( [0,1] \) which is impossible. One rule is to use the limit as \( 3 / N \).

Example: A poll of N = 100 person gives a probability of 0, then the confidence interval is \( [0, 0.03] \)

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