How to state null & alternative hypotheses

Question

Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample of 200 adults given medication B still had hives 30 minutes after taking the medication. The hypothesis test is to be carried out at a 1% level of significance.

1. State the null and alternative hypotheses in words and in statistical symbols. (3 points)
2. What statistical test is appropriate to use? Explain the rationale for your answer. (3 points)
3. Would the test be right-tailed, left-tailed or two-tailed? Explain the rationale for your answer. (3 points)

I believe this is a right tailed test but want to know what the null & alternative would be?

could it be p1=p2 & p1(B)>p2(A) or p1=p2 & p1(A) < p2 (B)?

Answer 1

"The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window"

First, to determine the alternate hypothesis (as researchers we would like to determine if a statistical relationship exists), we must direct attention to the above excerpt. Since the manufacturer wants to see if medication B is MORE effective than the standard medication A, the alternate hypothesis would be as follows: medication B is more effective than medication A. In other words, p1 (B) > p2 (A).

Therefore, the null hypothesis would be as follows: the effectiveness of medication B and medication A do not differ. In other words p1(B) = p2 (A).