Answer: [tex]0.311<p<0.489[/tex]
Step-by-step explanation:
The confidence interval for population proportion is given by :_
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
Given : n= 200 and x= 80
Then, [tex]\hat{p}=\dfrac{80}{200}=0.4[/tex]
Significance level : [tex]\alpha=1-0.99=0.01[/tex]
Critical value = [tex]z_{\alpha/2}=\pm2.576[/tex]
Then, the 99% confidence interval of the population proportion will be :-
[tex]0.4\pm (2.576)\sqrt{\dfrac{0.4(1-0.4)}{200}}\\\\\approx0.4\pm0.089\\\\=(0.311, 0.489 )[/tex]
Hence, the 99% confidence interval of the population proportion :_
[tex]0.311<p<0.489[/tex]
