因為信賴區間的敘述在說明樣本所獲得的訊息是很有用的方法, 如果只是記住公式, 可能容易有誤解. 下面對於 $\mu$ 95% 信賴區間的敘述,

1.
信賴區間 $(\overline{X}-1.96\sigma/\sqrt{n}, \overline{X}+1.96\sigma/\sqrt{n})$ 是一個隨機區間, 可能涵蓋參數 $\mu$.
2.
$\displaystyle P\biggl [ \overline{X}-1.96\frac{\sigma}{\sqrt{n}}<\mu< \overline{X}+1.96\frac{\sigma}{\sqrt{n}} \biggr ] =.95$指得是在長期的重覆抽樣之下, 此機率說明約有 95%的區間會涵蓋 $\mu$.
3.
當觀察到一個 $\overline{x}$, 則實際區間
$\displaystyle\biggl ( \overline{x}-1.96\frac{\sigma}{\sqrt{n}}, \overline{x}+1.96\frac{\sigma}{\sqrt{n}}\biggr )$,
將被視為 $\mu$ 的 95% 信賴區間.
4.
In any application we never know if the 95% confidence interval covers the unknown mean $\mu$. Relying on the long run relative frequency of coverage in property 2, we adopt the terminology confidence once the interval is calculate.

Definition of a Confidence Interval for a Parameter

An interval (L,U) is a $100(1-\alpha)\%$ confidence interval for a parameter if $P[L<\mbox{parameter}<U]=1-\alpha$ and the endpoints L and U are computable from the sample.