During an independent research, 2500 randomly selected people were interviewed whether they visit their dentist for a regular dental checkup or not. Only 1750 gave a positive answer. Calculate a 90% two-sided confidence interval on the proportion of people who regularly have a dental checkup. Round your answers to three decimal places

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= 2500Number of people gave a positive answer = 1750Then , 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]