If I have a drug purported to lower heart rate and I give it to a group of volunteers, I would conduct a paired t-test to determine if their HR before is lower than their HR after taking the drug.
I find significant results, so now I accept the premise that the drug lowers HR.
Now, what if I conduct the same experiment, except I have two groups to whom I give the drug. One of these groups is different in one way (say, overweight) and the other group is not. Otherwise, they are completely controlled.
If I want to test that the decrease in heart rate is more significant in group A compared to the decrease in heart rate in group B (i.e. group A's HR dropped more than group B), I would use an unpaired t-test. Is that correct the correct usage of a paired vs. unpaired t-test?