# Express the confidence interval (0.080, 0.150) in the form of hat p - E < p < hat p + E.

## Question:

Express the confidence interval {eq}(0.080,\ 0.150) {/eq} in the form of {eq}\hat p - E < p < \hat p + E {/eq}.

## Confidence interval for Proportion

Confidence interval can be expressed with two elements: proportion and margin of error. They are denoted by {eq}p {/eq} and {eq}E {/eq}. It always lie between the range of zero and one.

From the question, we get

Lower limit, {eq}LL {/eq} = 0.080

Upper limit, {eq}UL {/eq} = 0.150

Now, we find the proportion, {eq}p {/eq} which is the average of two limits

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

{eq}p = \frac{0.080 + 0.150}{2} {/eq}

{eq}p {/eq} = 0.115

And we find the margin of error, {eq}E {/eq} which is the difference between the two limits and divided by 2.

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

{eq}E = \frac{0.150 - 0.080}{2} {/eq}

{eq}E {/eq} = 0.035

Hence, it is expressed as {eq}0.115 - 0.035 < p < 0.115 + 0.035 {/eq}.