Unsure what kind of hypothesis test to use

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In summary, the researchers conducted a study to test the effectiveness of a drug preventing a disease by randomly assigning 20 patients to receive the drug or a placebo. After 1 year, 2 out of 10 patients who took the drug contracted the disease, while 5 out of 10 in the placebo group contracted the disease. If every patient had an equal chance of contracting the disease, the probability of 2 out of 7 patients in the treatment group contracting the disease is unknown.
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das1
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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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  • #2
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?
 
  • #3
Hi, thank you! That's what I suspected, I appreciate the affirmation
 

Related to Unsure what kind of hypothesis test to use

1. What is a hypothesis test?

A hypothesis test is a statistical method used to determine whether there is enough evidence to reject or accept a null hypothesis. It involves collecting and analyzing data to make an inference about a population based on a sample.

2. How do I know which hypothesis test to use?

The choice of a hypothesis test depends on various factors such as the type of data, research question, and the distribution of the data. It is important to carefully consider these factors before selecting a hypothesis test to ensure accurate and reliable results.

3. What is the difference between a one-tailed and two-tailed test?

A one-tailed test, also known as a directional test, tests for a difference in one specific direction (e.g. greater than or less than). A two-tailed test, also known as a non-directional test, tests for a difference in any direction. The choice between these two types of tests depends on the research question and the hypothesis being tested.

4. Can I use a hypothesis test if I have a small sample size?

Yes, you can use a hypothesis test with a small sample size. However, it is important to note that with a small sample size, the results may not be as reliable compared to a larger sample size. It is recommended to consult with a statistician or use a sample size calculator to determine the appropriate sample size for your study.

5. What happens if my data violates the assumptions of the chosen hypothesis test?

If your data violates the assumptions of the chosen hypothesis test, the results may not be accurate or reliable. In such cases, it is recommended to use a different hypothesis test or consider transforming the data to meet the assumptions of the test. Consulting with a statistician can also be helpful in such situations.

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