3 In the Rancho Bernardo Study n37851213 participants report

3). In the Rancho Bernardo Study (n=3785),1,213 participants reported a BMI that was overweight or obese. Generate a 95% confidence interval for the true proportion of the study population that was overweight or obese.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.320475561          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.0075852          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.01486672          
lower bound = p^ - z(alpha/2) * sp =   0.305608842          
upper bound = p^ + z(alpha/2) * sp =    0.335342281          
              
Thus, the confidence interval is              
              
(   0.305608842   ,   0.335342281   ) [ANSWER]