Answer: [tex](0.685,0.715)[/tex]
Step-by-step explanation:
The confidence interval for population proportion is given by :-
[tex]p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]
Given : Sample size : n= 2500
Number of people gave a positive answer = 1750
Then , Proportion of people gave a positive answer =[tex]p=\dfrac{1750}{2500}=0.7[/tex]
Significance level :[tex]\alpha= 1-0.9=0.1[/tex]
Critical value : [tex]z_{\alpha/2}=1.645[/tex]
Now, the 90% two-sided confidence interval on the proportion of people who regularly have a dental checkup will be :-
[tex]0.7\pm (1.645)\sqrt{\dfrac{0.7(0.3)}{2500}}\\\\\approx0.7\pm0.015\\\\=(0.7-0.015,0.7+0.015)\\\\=(0.685,0.715)[/tex]
