MIDTERM TWO QUESTION 2 (55 points) You may use a combination of SPSS and Hand Calculations A randomized control blinded trial was conducted to evaluate the effectiveness of a new pain reliever. A total of 150 patients undergoing joint replacement surgery participated in the study: 50 patients were randomly assigned to receive a high dose of the new pain reliever, 50 patients were randomly assigned to receive a low dose of the new pain reliever, and 50 patients were assigned to receive the standard pain reliever following surgery. Patients were asked to report pain reduction on a pain scale and were classified as having "reduced pain" if they achieved a decrease of 3 or more scale points. The following data were observed in the trial: 26 patients receiving a high dose of the new pain reliever achieved reduced pain, 22 patients receiving a low dose achieved reduced pain, and 12 receiving the standard pain reliever achieved reduced pain. Conduct a 3 Independent Samples Test hypothesis test at alpha=0.05 and alpha=0.01 to investigate which pain treatment works best for joint replacement surgery. (a) (4 pts) State the Null and Alternate Hypothesis Ho: HA: (b) (12 pts) Fill in the Observed and Expected Values in the tables below. To receive full credit, you must show your calculations for the Expected Table. OBSERVED GROUP Reduced Pain No Reduced Pain High Dose Low Dose Standard EXPECTED GROUP Reduced Pain No Reduced Pain High Dose Low Dose Standard\fNext, you will conduct Step 2 Post-Hoc Analysis to follow up the results of your Step 1 alpha = 0.05 analysis. (f) (6 pts) State the Null and Alternate Hypotheses for the Post-Hoc Analysis (g) Demonstrate your ability to conduct a post-hoc analysis using only ONE pairwise comparison, The Low Dose compared to the Standard Pain reliever group. Show all your work (SPSS or Hand Calculations) (i) (5 pts) Provide the value of the test statistic (show hand calculation or SPSS): (ii) (3 pts) What is the uncorrected p value associated with your test statistic? (Provide a range if using the table or the exact value if using SPSS or online calculator) (iii) (5 pts) Do you reject or fail to reject the null hypothesis for this post-hoc analysis? Justify your answer using the computed test statistic and p values