Answer: [tex]0.644<p<0.774[/tex]
Step-by-step explanation:
The confidence interval for population proportion (p) is given by :-
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Given : Significance level : [tex]\alpha: 1-0.995=0.005[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.0025}= 2.80[/tex]
Sample size : n= 385
Sample proportion : [tex]\hat{p}=0.709[/tex]
Then , the 99.5% confidence interval for population proportion is given by :-
[tex]0.709\pm (2.80)\sqrt{\dfrac{0.709(1-0.709)}{385}}\\\\\approx0.709\pm0.065\\\\=(0.709-0.065,0.709+0.065)=(0.644,0.774)[/tex]
Hence, the 99.5% confidence interval for population proportion :
[tex]0.644<p<0.774[/tex]
