I can not solve the problem from my homework.
We conducted two experiments. In the first, there were 400 patients, and in the second, 250. In these experiments, the effects of various drugs were evaluated. The average weight of people in the two groups was compared using the t-test. The test of normality for the first group gave a p-value below the significance threshold, and for the second above the significance threshold (but the histogram was bell-shaped). Variance in groups differed by more than 30%. Is it possible to say that the experiments were compared incorrectly?
There are answer answers to choose, only one of them is correct:
- everything is bad, the distribution is not normal, we need a Wilcoxon test
- everything is bad, the samples have different variance and sizes, you cannot use the t-test
- the samples are large enough so that everything is fine
- everything is fine, p-value of one of the groups is larger than the threshold, so the result of the first group could be random, then the distribution is still normal
Personally, I think that the correct answer is the second, because the condition for the applicability of the t-test is homogeneity of variance, and in these experiments it is very different. But I'm not sure that this is the right answer.