Problem 4. We want to test whether a treatment improve the condition of patients under certain period of time. The following scores show how the severity of the conditions of the patients changes (smaller scores indicating better conditions). Patient 1 2 3 4 5 6 7 8 9 10 11 12131415 before treatment 11 13 23 25 25 26 27 34 48 49 57 58 64 91 100 after treatment 10 12 49 20 25 25 21 51 26 23 52 54 55 79 95 difference 1 1 26 5 0 1 6 17 22 26 5 4 9 12 5 sign + + + . + + + + + + + + + rank 2 2 13.5 6 . 2 8 11 12 13.5 6 4 9 10 6 (a) (5 points) Perform a sign test to see whether the treatment is effective. Cal culate the pvalue for the test and report your conclusion using signicance level a = 0.05. PSTAT 1200 3 (b) (5 points) Calculate the value of the appropriate test statistic for the Wilcoxon signedrank test for doing the same comparison. Make a decision using the table provided from textbook. (0) (3 points) Calculate the value of the appropriate test statistic for the Wilcoxon signedrank test based on normal approximation. What is the distribution of this test statistics under the null hypothesis? ((1) (2 points) In general, which of the two tests, sign test or Wilcoxon signed rank test, will have more power if the treatment is effective? Explain your reasoning