Let's practice on finding the pooled proportion. For the following questions, please calcutate the pocled proportion \( p \) and \( q \). You may assume that the two grovps come from the same population:
1) A new medication for treating a particular allment is to be compared to a standard medication to see if there is any exdence that the proportion of complete cures is hidher for the new medleation. A 0.01 stgnificance level is chosen for a hypothests test. In a shingle random sample of 200 subjects, the new medication is found to produce 140 complete cures; in a simple random sample of 300 subjects, the standard medication is found to produce 180 complete cires.
2) A swimming school wants to determine whether a recently hired instructor ls working out. 16 out of 25 of instructor Als students passed the lifeguard certification test on the frist try, In comparison, 57 out of 72 of more experienced instructor B's students passed the test on the frist try.
3) Two types of medication for hlves are beling tested to determine if there is a difference in the percentage of edult patient reactions. Twenty out of a random sample of 200 aduts given medleation \( A \) stilil had hives 30 minutes after taking the medication. Twelve out of another random sample of 200 sadits given medication \( B \) stilil had hives 30 minutes after taling the medication.