95 What type of educational background do CEOs have In one s

9.5. What type of educational background do CEOs have? In one survey, 344 CEOs of medium and large companies were asked whether they had an MBA degree. There were 97 MBAs. Estimate with 95% confidence the proportion of all CEOs of medium and large companies who have MBAs.

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.281976744          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.024260329          
              
Now, for the critical z,              
alpha/2 =   0.025          
Thus, z(alpha/2) =    1.959963985          
Thus,              
Margin of error = z(alpha/2)*sp =    0.04754937          
lower bound = p^ - z(alpha/2) * sp =   0.234427374          
upper bound = p^ + z(alpha/2) * sp =    0.329526115          
              
Thus, the confidence interval is              
              
(   0.234427374   ,   0.329526115   ) [ANSWER]