In a random sample of 100 observations p bar 02 The 9544 Con

In a random sample of 100 observations, p bar= 0.2. The 95.44 Confidence interval for P is.. Please show how to solve

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.2          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.04          
              
Now, for the critical z,              
alpha/2 =   0.0228          
Thus, z(alpha/2) =    1.999077215          
Thus,              
Margin of error = z(alpha/2)*sp =    0.079963089          
lower bound = p^ - z(alpha/2) * sp =   0.120036911          
upper bound = p^ + z(alpha/2) * sp =    0.279963089          
              
Thus, the confidence interval is              
              
(   0.120036911   ,   0.279963089   ) [ANSWER]