A drug company has developed a new painkiller for chronic pains, although it is doubtful whether the new drug actually has any effect. The company conducts a double-blind experiment with n = 298 randomly chosen chronic pain patients over a 6 months period. All patients receive the drug for 3 consecutive months and the placebo for 3 consecutive months, but the order of the drug/placebo treatment is unknown to them and to the administering doctor. During the two 3 months periods, patients report their level of pain on a scale from 0 to 10 (higher numbers indicate more pain). For each patient, let di be the difference in the level of pain between the placebo treatment period and the drug treatment period (such that positive values of di indicate that the patient felt better while taking the drug).

(a) The outcome of the trial is such that    2:9 Will the company get the drug approved by the FDA based on this study, using a two sided hypothesis test?

(b) Suppose getting the drug approved yields profits of $600 million, while conducting a study as described above costs $10 million.

(b1) If the drug company knows that the new drug has no effect, would it still make sense for the company to conduct a study in the hope of finding an effect at the 5% significance level? Compute the expected profit of such a strategy.