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The degree of certainty, or the confidence level, is usually presented as a percent value. It refers to the reliability of the analysis to produce accurate intervals. For example, if $10$ confidence intervals are produced using different samples of the same size with $90%$ confidence, then $9$ out of $10$ intervals are expected to contain the actual mean.

For a $99%$ confidence interval, there is a $1%$ probability of observing a value outside this area. Because the distribution is symmetric, half of this area will be on each tail of the distribution.

A confidence interval for the population mean can be found by adding and subtracting the maximum error of estimate $E$ to and from the sample mean $xˉ.$

$CI=xˉ±E$

It is worth noting that increasing the level of confidence results in a wider interval that is more likely to catch the true mean, but it will be less precise because it will cover a greater range of values. This means there is a trade-off between confidence and precision.