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 = 4, the mean grade of group B is 69 points, a = 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 (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 1-0-i 511-145 (d) Assume that sample sizes are equal. What group size should be considered to obtain = 0.1 if the true difference in means is 3? We should use n ==