20 Researchers want to test the effectiveness of a new pain

#20 Researchers want to test the effectiveness of a new pain medication. Four hundred people were recruited to participate in the clinical trial. In clinical testing, 54 out of 201 people taking the medication reported pain symptoms. Of the other 199 people receiving a placebo, 20 reported pain symptoms. Combining the two samples together, what is the overall proportion of those who reported pain symptoms among all participants?

Solution

here n1=201,p1=54 ,therefore proportion of pain symptom takin medicanion P1=54/201

n2=199,p2=20 therefore proportion of pain in placebo P2=20/199

overall proportion of those who reported pain symptom P =(p1+p2)/(n1+n2)=(54+20)/(199+201)=74/400=0.185