a political analyst fond that 47 of 325 Republican voters in

a political analyst fond that 47% of 325 Republican voters in a survey thougt that the federal government had too much power. Find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.47          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.027685042          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp =   0.415738315          
upper bound = p^ + z(alpha/2) * sp =    0.524261685          
              
Thus, the confidence interval is              
              
(   0.415738315   ,   0.524261685   ) [ANSWER]