In a study of the relationship between pet ownership and physical activity in older adults, 619 subjects reported that they owned a pet, while 1904 reported that they did not. Give a 90% confidence interval for the proportion of older adults in this population who are pet owners. (Round your answers to three decimal places.)

Answer: (0.230,0.260)Step-by-step explanation:The confidence interval for proportion is given by :-[tex]p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}[/tex]Given : Number of subjects reported that they owned a pet = 619Number of subjects reported that they did not own a pet =1904Total subjects = [tex]n=619+1904=2523[/tex]Significance level : [tex]\alpha=1-0.9=0.1[/tex]The proportion that of older adults in this population who are pet owners :-[tex]p=\dfrac{619}{2523}\approx0.245[/tex]Now, the 90% confidence interval for the proportion of older adults in this population who are pet owners is given by :-[tex]0.245\pm z_{0.05}\sqrt{\dfrac{0.245(0.755)}{2523}}\\\\=0.245\pm(1.645)(0.009)\\\\=0.245\pm0.014805\\\\=(0.230195,0.259805)\approx(0.230,0.260)[/tex]