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# Express the confidence intervel (0.501, 0.609) in the from of p+E

Confidence intervals
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asked 2021-08-03
Express the confidence intervel (0.501, 0.609) in the from of $$\displaystyle{p}+{E}$$

## Answers (1)

2021-08-08

Step 1
Here we need to express the given confidence interval in $$\displaystyle{p}\frac{+}{{-{{E}}}}$$ form.
Step 2
a) Here the given $$\displaystyle{C}{I}={\left({0.501},{0.609}\right)}$$
From the given confidence interval.
Point estimate $$\displaystyle{p}={\frac{{{U}+{L}}}{{{2}}}}={\frac{{{0.501}+{0.609}}}{{{2}}}}$$
$$\displaystyle={0.555}$$
$$\displaystyle\therefore{p}={0.555}$$
Now $$\displaystyle{E}={\frac{{{U}+{L}}}{{{2}}}}={\frac{{{0.609}-{0.501}}}{{{2}}}}={0.054}$$
$$\displaystyle\therefore{E}={0.054}$$
$$\displaystyle\therefore{C}{I}={0.555}\pm{0.054}$$
$$\displaystyle={0.501}{<}{p}{<}{0.609}$$
$$\displaystyle{P}\pm{E}={0.555}\pm{0.054}$$

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