Question

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

Confidence intervals
ANSWERED
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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