In a survey of 1000 people 420 are opposed to the tax increa

In a survey of 1,000 people, 420 are opposed to the tax increase. Construct a 95 percent confidence interval for the proportion of those people opposed to the tax increase.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.42          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.01560769          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.030590511          
lower bound = p^ - z(alpha/2) * sp =   0.389409489          
upper bound = p^ + z(alpha/2) * sp =    0.450590511          
              
Thus, the confidence interval is              
              
(   0.389409489   ,   0.450590511   ) [ANSWER]