A random sample of busness graduates is selected from a local college. Their annual salary an thousand dollars) of one year and three years after graduation are recorded and shown below. ID 1 2 3 4 5 6 7 8 9 1 O 1 1 1 2 1 3 1 4 One year 44 45 45 47 44 47 44 46 47 44 47 45 46 47 Three years 44 49 51 53 47 49 48 48 51 46 52 50 52 51 Suppose that we want to test whether the median annual salary of three years after graduation is higher than one year after graduation for all busness graduates in this college. Part A State the null and alternative hypotheses. Let Md be the median difference in the annual salary between three years and one year after graduation for all busness graduates in this college. Note: The difference in the annual salary is defined as [Three years] [One year]. H0 1 Md = V 0 Ha I Md > v 0 Part B Determine the rank of the absolute difference in the annual salary between three years and one year after graduation. 1. The ranks of the absolute differences are separated by commas. 2. For example, Rank = (4, 2, 1, 3). So, you enter 4, 2, 1, 3 in the textbox. Rank = 6.5,12,12,4,2,6.5,2,6.5,2,9.5,9.5,12.6.5 Part C Suppose that we want to test the hypotheses with the signed rank test at the 5% significance level. The test statistic is . (Round the test statistic to 5 decimal places) Since the test statistic is larger v than the critical value, , we reject Ho v . Therefore, the sample data provide sufficient v evidence to support that the median annual salary of three years after graduation is higher than one year after graduation for all busness graduates in this college. . Part D Suppose that we want to approximate the p-value of the test statistic in the signed rank test using a normal distribution. Calculate z-score (Round the z-score to 5 decimal places) Calculate p-value (Round the p-value to 4 decimal places) Part E Suppose that we want to test the hypotheses with the sign test. The p-value is . (Round the test statistic to 4 decimal places) Part F Suppose that we want to approximate the p-value of the test statistic in the sign test using a normal distribution. Calculate z-score (Round the z-score to 5 decimal places) Calculate p-value (Round the p-value to 4 decimal places)