I have two samples I'd like to do a hypothesis test on. The sample proportions are:
$$
\hat{p}_1 = \frac{120}{4000}
$$
$$
\hat{p}_2 = \frac{9000}{300000}
$$
If I did a test of two proportions where the null is $p_1=p_2$, would there be issues because $n_1=4000$ and $n_2 = 300000$?
Best Answer
Similarity in sample size between groups is not an assumption for any hypothesis test for proportions that I'm familiar with. You should be fine to run the test.
Note: if you are planning a study, the study will be better powered (there will be a higher probability of finding a result if there is one) if the sample sizes in the two groups are similar. You don't want to plan a study and recruit 10 people in one group and 1000 in another group.