1. 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 record the time it takes until pain is resolved. Treatments are assigned in random order (i.e., some patients receive the currently available medication first and then the experimental medication and others receive the experimental medication first and then the currently available medication). The mean difference in times between the experimental and currently available medication is -9.4 minutes, with a standard deviation of 2.8 minutes. Construct a 95% confidence interval for the mean difference in times between the experimental and currently available medication.
2. A clinical trial is run comparing a new drug for high cholesterol to a placebo. A total of 40 participants are randomized (with equal assignment to treatments) to receive either the new drug or placebo. Their total serum cholesterol levels are measured after eight weeks on the assigned treatment. Participants receiving the new drug reported a mean total serum cholesterol level of 209.5 (std dev = 21.6) and participants receiving the placebo reported a mean total serum cholesterol level of 228.1 (std dev = 19.7).
a. Construct a 95% confidence interval for the difference in mean total serum cholesterol levels between participants receiving the new drug versus placebo.
b. Is the new drug effective? Justify briefly.