I am struggling with the below question The text is Basic St

I am struggling with the below question. The text is Basic Statistics for Business & Economics 8e

The Capital Area Transit Authority (CAT) wished to estimate the proportion of central city workers that use public transportation to get to work. A recent study reported that of 100 workers, 29 use public transportation. Develop a 95% confidence interval. *Use Appendix B.1 and round your answer to the nearest thousandth.*

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.29          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.045376205          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.96          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.201062638          
upper bound = p^ + z(alpha/2) * sp =    0.378937362          
              
Thus, the confidence interval is              
              
(   0.201   ,   0.379   ) [ANSWER]