A group of 20 people from New York and a group of 13 people from Los Angeles passed the same quiz. The mean grade of group A is 71 points, with the standard deviation of = 4, the mean grade of group B is 69 points, oz = 3. Use a = 0,05. Assuming that the subjects are chosen randomly, the cities' population are independent and the points are normally distributed: (a) Check if there is a significant difference between the mean grades of the groups, Find the P-value of this test. Round your answer to four decimal places (e.g. 98.7654). Round your answer to three decimal places (e.g. 98.765). P - value= (b) Explain how the test could be conducted with a confidence interval. Round your answers to three decimal places (e.g. 98.765). We are 95% confident that value 1 exceeds value 2 by between i SM- MS (c) What is the power of the test for the true difference in means of 3? Round your answer to three decimal places (e g. 98.765). The power of the test is I - 0 = i (d) Assume that sample sizes are equal. What group size should be considered to obtain / = 0. I'if the true difference in means is 3? We should use n = ni =