4 10 In a survey of 250 voters prior to an election 40 indic

4. [10] In a survey of 250 voters prior to an election, 40% indicated that they would vote for the incumbent candidate. Construct a 95% confidence interval for the population proportion of voters who support the incumbent.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.4          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.030983867          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.060727263          
lower bound = p^ - z(alpha/2) * sp =   0.339272737          
upper bound = p^ + z(alpha/2) * sp =    0.460727263          
              
Thus, the confidence interval is              
              
(   0.339272737   ,   0.460727263   ) [ANSWER]