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A confidence interval is a range for assessing an undetermined parameter in likelihood ratio statistics.

From one or both sides, it can be bounded. At a given confidence level, a confidence interval is calculated.

The $95$percent threshold is the most commonly utilized, however other amounts are occasionally used as well.

If the proportion of observed in a random sample of size $n$that relate to a class of interest is $\widehat{p}$, an estimate $100(1鈭�伪)\mathrm{\%}$confidence interval on the fraction $p$of the population which belongs to this class is

Equation $1$

$\widehat{p}鈭�z_{\frac{伪}{2}}\sqrt{\frac{\widehat{p}(1鈭�\widehat{p})}{n}}鈮�p鈮�\widehat{p}+z_{\frac{伪}{2}}\sqrt{\frac{\widehat{p}(1鈭�\widehat{p})}{n}}$

where $z\frac{伪}{2}$denotes the normally distributed distribution's top $\frac{伪}{2}$basis point.

Three hundred thirty-eight $(x=338)$of the $511$residences surveyed do not satisfy the minimal disaster preparedness guidelines.

As a result, the population mean of homes that do not meet the minimum earthquake preparedness standards is

$\widehat{p}=\frac{338}{511}=0.661$

For such a two-sided confidence interval of $90\%$

$\begin{array}{c}\frac{伪}{2}=\frac{1鈭�0.90}{2}=0.05,\\ \end{array}$

then

$z_{\frac{伪}{2}}=1.65.$

As a result of Equations $1$and $2$, the population proportion has a $90\%$two-sided CI.

role="math" localid="1649783275438" $\begin{array}{r}0.661鈭�1.65\sqrt{\frac{0.661(1鈭�0.661)}{511}}鈮�p鈮�0.661+1.65\sqrt{\frac{0.661(1鈭�0.661)}{511},}\\ 0.661鈭�0.0344鈮�p鈮�0.661+0.0344\end{array}$

As a result, $p$has a $90\%$CI.

$0.627鈮�p鈮�0.696$