For each of the problems that follow, you will be asked to conduct hypothesis tests. For each problem clearly state the hypothesis test to be conducted using proper notation. State the test score and the p- value. Say whether to reject or fail to reject the null hypothesis. Then clearly, in plain English and in the context of the problem, state your conclusion. Use a = 0.05 unless stated otherwise in the problem. 11. An experiment was conducted on patients with bipolar disorder. 55 patients received a new medication, while the control group of 60 patients received a placebo. Both patients were rated on the Young-Mania scale to measure their improvement. The experimental group had a mean improvement of 14.8 with a standard deviation of 12.5, while the control group had a mean improvement of 8.1 with a standard deviation of 12.7. Determine if the experimental group had a larger mean improvement than the control group with significance level a = 0.01. (13 points)