(a) A pharmaceutical company is conducting an experiment to test whether a new type of pain reliever is effective. In this context, a treatment is considered effective if it is successful with a probability of more than 0.5.

The pain reliever was given to 30 patients and it reduced the pain for 20 of them. You are asked to use an appropriate hypothesis test to determine whether the pain reliever is effective at the 5% significance level. Comment on your findings.

(b) A second experiment followed where a placebo pill was given to another group of 40 patients. A placebo pill contains no medication and is prescribed so that the patient will expect to get well.

In some situations, this expectation is enough for the patient to recover. This effect, known as the placebo effect, occurred to some extent in the second experiment where the pain was reduced for 21 of the patients. You are asked to consider an appropriate hypothesis test to incorporate this new evidence with the previous data and reassess the effectiveness of the pain reliever