A new experimental drug is given to patients suffering from severe migraine headaches. Patients report their pain experience on a scale of 1 – 10 before and after the drug. The difference of their pain measurement is recorded. If their pain decreases, the difference will be positive (+), if the pain increases, the difference will be negative (−). The data are ignored if the difference is 0. Under the null hypothesis that the drug is ineffective and there is no difference in pain experience before and after the drug, the number of +’s will have a binomial distribution with n equal to the number of +’ s and −’s; and p = 1/2. This is the basis of a statistical test called the sign test. Suppose a random sample of 20 patients are given the new drug. Of 16 nonzero differences, 12 report an improvement (+). If one assumes that the drug is ineffective, what is the probability of obtaining 12 or more +’s, as observed in these data? Based on these data do you think the drug is ineffective?