MHB Unsure what kind of hypothesis test to use

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The discussion revolves around determining the appropriate hypothesis test for evaluating a drug's effectiveness in preventing disease. Researchers conducted a study with 20 patients, where 10 received the drug and 10 received a placebo, resulting in 2 and 5 disease cases, respectively. The probability of contracting the disease is estimated at p=7/20, and the binomial distribution can be used to calculate the likelihood of 2 patients from the treatment group contracting the disease. Participants confirm that this approach is valid, providing reassurance to the original poster. The conversation emphasizes the need for understanding binomial distribution in hypothesis testing for clinical studies.
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The problem:

Researchers conduct a study to test the effectiveness of a drug preventing a disease. Of 20 patients in the study, 10 are randomly assigned to receive the drug and 10 to receive a placebo. After 1 year, suppose 5 patients in the control group contract the disease, while 2 patients who took the drug contract the disease.

For those who took the drug: 2 got the disease, 8 no disease.
For those who took placebo: 5 got the disease, 5 no disease.

If the drug is not effective, then every patient is equally likely to contract the disease. In that case, if 7 patients out of 20 contract the disease, what is the probability that 2 of them are in the treatment group? Also, what is the probability that 2 or fewer are in the treatment group?

So I don't know anything about the distribution, I also don't know what the probability of each patient getting the disease is. It almost seems like a binomial problem but I don't think I have enough info. If anyone can help me figure out how to approach this that would be much appreciated!
 
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das said:
The problem:

Researchers conduct a study to test the effectiveness of a drug preventing a disease. Of 20 patients in the study, 10 are randomly assigned to receive the drug and 10 to receive a placebo. After 1 year, suppose 5 patients in the control group contract the disease, while 2 patients who took the drug contract the disease.

For those who took the drug: 2 got the disease, 8 no disease.
For those who took placebo: 5 got the disease, 5 no disease.

If the drug is not effective, then every patient is equally likely to contract the disease. In that case, if 7 patients out of 20 contract the disease, what is the probability that 2 of them are in the treatment group? Also, what is the probability that 2 or fewer are in the treatment group?

So I don't know anything about the distribution, I also don't know what the probability of each patient getting the disease is. It almost seems like a binomial problem but I don't think I have enough info. If anyone can help me figure out how to approach this that would be much appreciated!

Hi das! (Wave)

That is exactly right.
Based on the evidence, the estimate that someone contracts a disease will be p=7/20, and the binomial distribution can then predict how many people out of n=10 will contract the disease.
What is the probability that 2 people will contract the disease?
 
Hi, thank you! That's what I suspected, I appreciate the affirmation
 

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