Efan Halliday

2021-09-23

Express the confidence interval $53.5\mathrm{%} in the form of $\stackrel{^}{p}±ME\stackrel{^}{p}±ME$

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Step 1
Solution
Given:
Confidence interval in the trilinear inequality form:
Lower limit $ Upper limit
$53.5\mathrm{%}
Hence,
Lower limit $=53.5\mathrm{%}$
Upper limit $=69.7\mathrm{%}$
Step 2
Sample proportion $\left(\stackrel{^}{p}\right)=\frac{\text{Upper limit+Lower limit}}{2}$
Plug in all the values in the formula, we get
Simple proportion $\left(\stackrel{^}{p}\right)=\frac{69.7\mathrm{%}+53.5\mathrm{%}}{2}$
Sample proportion $\left(\stackrel{^}{p}\right)=61.6\mathrm{%}$
Step 3
Margin of error $\left(ME\right)=\frac{\text{Upper limit+Lower limit}}{2}$
Plug in all the values in the formula, we get
Margin of error $\left(ME\right)=\frac{69.7\mathrm{%}+53.5\mathrm{%}}{2}$
Margin of error $\left(ME\right)=8.1\mathrm{%}$
Step 4
Express the confidence interval in the form $\left(\stackrel{^}{p}\right)±E$
$\left(\stackrel{^}{p}\right)±E-61.6\mathrm{%}±8.1\mathrm{%}$

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