# 8.3.1 - Confidence Intervals

Recall the general form of a confidence interval...

$$sample\ statistic\pm\underbrace{(multiplier)\ (standard\ error)}_{\textbf{margin of error}}$$.

The formula for constructing a confidence interval for the difference in paired means is almost identical to the formula for constructing a confidence interval for one mean. Note that the only change is the subscript d which stands for difference.

Confidence Interval for the Difference Between Two Paired Means
$$\underbrace{\overline{x}_d}_{\text{sample statistic}} \pm \overbrace{t^*}^{\text{multiplier}} \underbrace{\left(\dfrac{s_d}{\sqrt{n}}\right)}_{\text{standard error}}$$
$$t^*$$ is the multiplier with $$df = n-1$$