Say I’m analyzing whether a drug works.
My test statistic is the amount of days taken to recover.
I split a group of 100 into two, and give one the drug and the other a placebo.
So my null hypothesis is that there is no difference between both groups, and my alternate hypothesis is that the group given the real drug recovers quicker.
If I analyse the time taken to recover, repeating the process 10,000 times and plot it on a graph, using the test statistic of X bar of the control group - X bar of the drug group, I would notice an average sample mean of say 4 days. Why should this be a mean of 0? Surely on average the drug group would recover quicker?