Suppose the manufacturer of Advil a common headache remedy r

Suppose the manufacturer of Advil, a common headache remedy, recently developed a new formulation of the drug that is claimed to be more effective. To evaluate the new drug, a sample of 260 current users is asked to try it. After a one-month trial, 239 indicated the new drug was more effective in relieving a headache. At the same time a sample of 380 current Advil users is given the current drug but told it is the new formulation. From this group, 343 said it was an improvement.

Solution

Let p1 = new drug approval proportion
p2 = current drug approval proportion

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0  

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 = 239/260 =   0.919230769      
p2 = x2/n2 = 343/380 =    0.902631579      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.022734194      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    0.730142023      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.644853627      
          
Also, the p value is          
          
P =    0.232651688      
          
As |Z| < 1.6449, and P > 0.05, then we    FAIL TO REJECT THE NULL HYPOTHESIS.

Hence, there is no significant evidence that the new formulation is more effective than the old formulation at 0.05 level. [CONCLUSION]