A consumer agency wanted to find out if the mean time taken by each of three brands of medicines to provide relief from a headache is the same. The first drug was administered to six randomly selected patients, the second to four randomly selected patients, and the third to five randomly selected patients. The following table gives the time (in minutes) taken by each patient to get relief from a headache after taking the medicine. Drug I Drug II Drug III 25 15 44 38 21 39 42 19 54 65 25 58 47 73 52 (a) At the 2.5% significance level, will you conclude that the mean time taken to provide relief from a headache is the same for each of the three drugs? (b) What assumptions did you make for performing the test?