In a recent presidential election 611 voters were surveyed a

In a recent presidential election, 611 voters were surveyed and 308 of them said that they voted for the candidate who won (based on data from the ICR Survey Research Group). Find the point estimate of the percentage of voters who said that they voted for the candidate who won. Find a 98% confidence interval estimate of the percentage of voters who said that they voted for the candidate who won. Of those who voted, 43% actually voted for the candidate who won. Is this result consistent with the survey results? How might a discrepancy be explained?

Solution

a)

Note that              
              
p^ = point estimate of the population proportion = x / n

= 308/611

=    0.504091653 = 50.409% [ANSWER]

***************************          

b)
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.020227158          
              
Now, for the critical z,              
alpha/2 =   0.01          
Thus, z(alpha/2) =    2.326347874          
Thus,              
Margin of error = z(alpha/2)*sp =    0.047055405          
lower bound = p^ - z(alpha/2) * sp =   0.457036248          
upper bound = p^ + z(alpha/2) * sp =    0.551147058          
              
Thus, the confidence interval is              
              
(   45.7036248%   ,   55.1147058%   ) [ANSWER]

****************************

c)

As 43% is not inside the interval, then no, this is not consistent with the interval.

This discrepancy may be because of a certain bias in sampling, or insufficient sample size.