A hospital wants to determine whether a new pain management therapy is more effective than the standard therapy in reducing post-surgical pain. Two groups of patients are randomly assigned to either the new therapy or the standard therapy. After 24 hours, their pain levels are measured on a scale from 0 (no pain) to 100 (severe pain). The hospital wants to test if the new therapy reduces pain more effectively than the standard therapy. The data is found in the accompanying data file. Use α = 0.05 for all calculations. Download .csv file Let μ represent the average pain level, and μNT be the mean pain level of the new theraphy. (a) Construct the most appropriate statistical hypotheses that whether a new pain management therapy is more effective than the standard therapy in reducing post- surgical pain. OA. Ho μNT-ST>0 HA μNT - μST<0 B. Ho PNT - PST=0 HANT - PST < 0 C. Ho D. Ho NT μNT - ST=0 PST 0 HA MNT - μST > 0 HA PNT - µST < 0 - E. Ho PNT PST 20 HA PNT - μST > 0 (b) Does there appear to be a difference in the variation in the pain level between the new and the standard therapy? A. There appears to be equal variation in the pain level between the new and the standard therapy. B. There appears to be more variation in the pain level between the new and the standard therapy. C. There appears to be less variation in the pain level between the new and the standard therapy. D. There appears to be unequal variation in the pain level between the new and the standard therapy. (c) Report the p-value of the test you ran in part (b), the Test for Equal Variances. Use at least three decimals in your answer. P-value = (d) Test the statistical hypotheses in part (a), testing for the average pain level between two therapies. Find the value of the test statistic for this test. Use at least two decimals in your answer. Test Statistic = (e) Determine the P-value of your statistical test in part (d), and report it to at least three decimal places. P (f) Determine the appropriate degrees of freedom for the test in part (d). Use at least 3 digits after the decimal. DF= (g) Using an α of 5%, this data suggest that the null hypothesis should ? The pain level of the new therapy is ? when compared to the standard therapy.