In a trial of 200 patients who received 10 MG doses of a dai

In a trial of 200 patients who received 10 MG doses of a daily drug, 28 reported headache as a side effect. The point estimate for the poulation proportion is 0.14. I need to construct a 90% confidence interval for the population proportion of patients who received the drug and report headache as a side effect. I am lost, don\'t know how to get Z sub alpha. please explain all steps and I appreciate your help greatly

Solution

Note that              
              
p^ = point estimate of the population proportion = x / n =    0.14          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.024535688          
              
Now, for the critical z,              
alpha/2 =   0.05          

Thus, by using table/technology,

z(alpha/2) =    1.644853627          

Thus,              
Margin of error = z(alpha/2)*sp =    0.040357616          
lower bound = p^ - z(alpha/2) * sp =   0.099642384          
upper bound = p^ + z(alpha/2) * sp =    0.180357616          
              
Thus, the confidence interval is              
              
(   0.099642384   ,   0.180357616   ) [ANSWER]