Question

9.1.13 0 088, upper bound 0.312, 1200 The point estimate of the population proportion is Round to the nearest thousandth as needed )

Answer 1

Solution :

$\mathrm{Given\::}$

$\mathrm{Lower\:bound}=0.088$

$\mathrm{Upper\:bound}=0.312$

$\mathrm{n=1200}$

$\mathrm{Now,}$

$\mathrm{Point\:estimate\:of\:the\:population\:proportion\:\:}(\hat{p})=\frac{\mathrm{lower\:bound+upper\:bound}}{2}$

$\hat{p}=\frac{0.088+0.312}{2}=\frac{0.4}{2}=0.2\approx 0.200$

$\mathrm{and}$

$\mathrm{Margin\:of\:error\:\:(E)=\frac{\mathrm{upper\:bound-lower\:bound}}{2}=\:\frac{0.312-0.088}{2}\:=\:\frac{0.224}{2}\:=\:0.112}$

$\mathrm{Hence,}$

$\mathrm{Point\:estimate\:of\:the\:population\:proportion\:is\:\:\bold{0.200}}$

$\mathrm{Margin\:of\:error\:(E)\:=\:\bold{0.112}}$