# Express the confidence interval (83.2%, 96.6%) in the form of p plus or minus ME.

## Question:

Express the confidence interval {eq}(83.2\%,\ 96.6\%) {/eq} in the form of {eq}p \pm ME {/eq}.

## Expressing the confidence interval

The confidence interval is generally expressed in the form proportion plus or minus margin of error. In symbols form,

{eq}p \pm E {/eq}

Where {eq}p {/eq} is the proportion and {eq}E {/eq} is the margin of error.

First, we calculate the proportion, {eq}p {/eq} and margin of error, {eq}E {/eq}

We are given the confidence limits. The lower limit, {eq}LL {/eq} = 0.832 and upper limit, {eq}UL {/eq} = 0.966

{eq}p = \frac{UL + LL}{2} {/eq}

{eq}p = \frac{0.966 + 0.832}{2} {/eq}

{eq}p {/eq} = 0.899

And the margin of error, {eq}E {/eq}

{eq}E = \frac{UL - LL}{2} {/eq}

{eq}E {/eq} = 0.067

Hence, in the form 0.899 {eq}\pm {/eq} 0.067.