Suppose 1654 of 2056 registered voters sampled said they pla

Suppose 1,654 of 2,056 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest tenth of a percent)?

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.804474708          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.008746738          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.017143291          
lower bound = p^ - z(alpha/2) * sp =   0.787331417          
upper bound = p^ + z(alpha/2) * sp =    0.821617999          
              
Thus, the confidence interval is              
              
( 78.7% , 82.2% ) [ANSWER]