Question: Suppose you would like to test the hypothesis that "taking statistics courses makes you more intelligent." To do so, you devise a test that measures overall intelligence and administer it to students at Berkeley. You make an observational study where some of these students have taken statistics and some have not.

1. What is your treatment group? What is your control group? Treatment: students that have taken statistics courses. Control: students that have not taken statistics courses.
2. You conduct a hypothesis test for the difference in test scores between the two groups with a null hypothesis that says there is no difference and an alternative hypothesis that says students who take stats classes are smarter. Your p-value is 0.001. What can you conclude? What can’t you conclude? Assume the significance level is 5%. We can conclude that there is a highly significant difference among the groups that doesn’t seem to be explained by chance (assuming the the sample is random, and there is no bias). However, we don’t know which group scored higher than the other. And even if the treatment group showed a larger score, we can’t conclude that taking statistics courses makes them more intelligent.
3. Is there a way to answer the question you are interested in given the setup of your experiment? If so, why? If not, what would you change to answer the question?

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