Consider the following two scenarios

**(1)** An experiment tests the effect of a new medicine on people which have a certain illness. The conclusion of the experiment is that for 5% of the people tested the medication led to improvement while for 95% it had no effect. (The experiment followed all rules: it had a control test it was double blind etc. …)

A statistical analysis concluded that the results are statistically significant, where the required statistical significance level is 1%. This roughly means that the probability that such an effect happend by chance (under the “null hypothesis”) is less or equal 0.01. (This probability is called the -value. Suppose that = 0.008.)

**(2)** An experiment tests the effect of a new medicine on people which have a certain illness. The conclusion of the experiment is that for 30% of the people tested the medication led to improvement while for 70% it had no effect. (The experiment followed all rules: it had a control test it was double blind etc. …)

A statistical analysis concluded that the results are statistically significant, where the required statistical significance level is 1%. (Again, this roughly means that the probability that such an effect happend by chance (under the “null hypothesis”) is less or equal 0.01. And again suppose that = 0.008.)

**Test your intuition:** In which of these two scenarios it is more likely that the effect of the medication is real.

You can assume that the experiments are identical in all other terms that may effect your answer. E.g., the theoretical explanation for the effect of the medicine. Note that our assumption is likely to imply that the sample size for the first experiment is larger.