3. (10 points) 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 = 19.1). A 95% condence interval for npiqcebo \"new drug, the difference in mean total serum cholesterol levels between participants receiving the placebo and participants receiving the new drug is (4.92, 32.23). Is the new drug effective? If so. how much more effective, on average, is the new drug compared to placebo? Justify your answers. A study was conducted to estimate the mean total cholesterol level in children 2-6 years of age. A sample of 9 participants is selected and their total cholesterol levels are measured as follows. 185 225 240 196 175 180 194 147 223 The sample mean is 196 and the sample variance is 841. a) Obtain a 95% confidence interval for the mean total cholesterol level in the population of children 2-6 years of age. b) Interpret the 95% confidence interval. 2. (10 points) A crossover trial was 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, patient's 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 and interpret a 95% confidence interval for the difference in mean times to pain relief between the experimental and currently available medication