Question

If n=590 and p=0.93, construct a 90\% confidence interval.

Confidence intervals
ANSWERED
asked 2021-08-01
If \(\displaystyle{n}={590}\) and \(\displaystyle{p}={0.93}\), construct a \(\displaystyle{90}\%\) confidence interval.

Expert Answers (1)

2021-08-03
Step 1
Express the expression for the confidence interval.
\(\displaystyle{C}.{I}={p}\pm{Z}\cdot\sqrt{{{\frac{{{p}{\left({1}-{p}\right)}}}{{{n}}}}}}\)
Here, Z* is the critical value .
From the Z table, the value corresponding to the region 90.5 is,
\(\displaystyle{Z}\cdot={1.31}\)
Step 2
Put 590 for n, 0.93 for p, 1.31 for Z* implies,
\(\displaystyle{C}.{I}={0.93}\pm{1.31}\sqrt{{{\frac{{{0.93}{\left({1}-{0.93}\right)}}}{{{0.93}}}}}}\)
\(\displaystyle{C}.{I}={0.93}\pm{0.346}\)
Thus, the confidence interval is \(\displaystyle{0.93}+{0.346}\) and \(\displaystyle{0.93}-{0.346}\).
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