a crossover trial is conducted to compare an experimental medication for migraine headaches to a currently available medication. A total of 50 patients are enrolled in the study and each patient receives both treatments. The outcome is the time, in minutes, until the headache pain resolves. Following each treatment, patients recode the time it takes until pain is resolved. Treatments are assigned in random order(ie., some patients receive the currently available medication first and then the experimental medication, and others receive the experimental medication first then the currently available medication). The mean difference in times between the experimental and currently available medication of 2.8 minutes. Construct a 95% CI for the mean difference in times between the experimental and currently available medication.
Suppose in the study describe in the first question each patient was also asked if the assigned medication caused any stomach upset. Among the 50 patients, 12 reported stomach upset with the experimental medication. Construct a 90% CI for the proportion of patients who experience stomach upset with the experimental medication.