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# Confidence Intervals

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Confidence Intervals

confidence interval, centered on the mean of your sample, is the range of values that is expected to capture the population mean with a given level of confidence.

Calculate the confidence interval by combining the sample mean with the margin of error, found by multiplying the standard error of the mean by the z- score of the percent confidence level:

confidence intervalmargin of error=x¯¯¯±margin of error=Za2×σn\begin{align*}\text{confidence interval} &= \overline{x} \pm \text{margin of error}\\ \text{margin of error} &= Z_{\frac{a}{2}} \times \frac{\sigma}{\sqrt{n}}\end{align*}

Important Note: The confidence level indicates the number of times out of 100 that the mean of the population will be within the given interval of the sample mean, not the probability that the mean of the population will be in that interval.

Here are the z-scores for some common confidence levels.

 Confidence Level Z-Score 90% 1.645 95% 1.96 98% 2.326 99% 2.576

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