Answer:
point estimate=p=0.77
95 % confidence interval= [0.732,0.808]
Step-by-step explanation:
Let p be the point estimate of rho. The point estimate can be computed as
p=x/n
p=365/474
p=0.77.
The 95% confidence interval for rho can be computed as
[tex]p-z_{\frac{\alpha}{2} } \sqrt{\frac{pq}{n} }<rho<p+z_{\frac{\alpha}{2} } \sqrt{\frac{pq}{n} }[/tex]
where,
p=0.77
q=1-p=1-0.77=0.23
[tex]z_{\frac{\alpha}{2} } =z_{\frac{\0.05}{2} } =z_{0.025 } =1.96[/tex]
[tex]0.77-1.96 \sqrt{\frac{0.77(0.23)}{474} }<rho<0.77+1.96 \sqrt{\frac{0.77(0.23)}{474} }[/tex]
[tex]0.77-1.96(0.0193)<rho<0.77+1.96(0.0193)[/tex]
[tex]0.77-0.0378<rho<0.77+0.0378[/tex]
[tex]0.732<rho<0.808[/tex] (rounded to three decimal places).
