95 Compute the 95 confidence interval estimate of a populati

9.5. Compute the 95% confidence interval estimate of a population proportion when the sample proportion is .6 and the sample size is 400.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.6          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.024494897          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.048009117          
lower bound = p^ - z(alpha/2) * sp =   0.551990883          
upper bound = p^ + z(alpha/2) * sp =    0.648009117          
              
Thus, the confidence interval is              
              
(   0.551990883   ,   0.648009117   ) [ANSWER]