To illustrate a confidence interval, suppose a sample of $20$ university students provides a mean calorie estimate for a cookie of $200$, with a $95\%$ confidence interval ranging from $160$ to $240$. This indicates that there is a high probability ($95\%$) that the true mean calorie estimate for the entire population of university students falls somewhere between $160$ and $240$. Furthermore, this interval allows for hypothesis testing; any hypothetical population mean outside of this $160$ to $240$ range (such as a hypothetical value of $250$) would be considered statistically significantly different from the sample mean at the $.05$ alpha level.