# The Excel function: CONFIDENCE.NORM

## Description

The confidence interval is a range of values. Your sample mean, x, is at the center of this range and the range is x ± CONFIDENCE.NORM. For example, if x is the sample mean of delivery times for products ordered through the mail, x ± CONFIDENCE.NORM is a range of population means. For any population mean, μ_{0}, in this range, the probability of obtaining a sample mean further from μ_{0} than x is greater than alpha; for any population mean, μ_{0}, not in this range, the probability of obtaining a sample mean further from μ_{0} than x is less than alpha. In other words, assume that we use x, standard_dev, and size to construct a two-tailed test at significance level alpha of the hypothesis that the population mean is μ_{0}. Then we will not reject that hypothesis if μ_{0} is in the confidence interval and will reject that hypothesis if μ_{0} is not in the confidence interval. The confidence interval does not allow us to infer that there is probability 1 – alpha that our next package will take a delivery time that is in the confidence interval.