Construct a confidence interval of the population proportion

Construct a confidence interval of the population proportion at the given level of confidence.

X=540, n=1100, 95% confidence

The upper bound of the confidence interval is_____

The lower bound of the confidence interval is_____

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.490909091          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.015073075          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.461366406 [ANSWER]
upper bound = p^ + z(alpha/2) * sp =    0.520451775 [ANSWER]