3. A team of psychologists designed a study in which 12 psychiatric patients diagnosed as having generalized anxiety disorder were randomly assigned to one of three new types of therapy, here labeled X, Y, and Z. One year after therapy, the patients' overall mental health scores were as follows: 2 Mental Health Assessment Therapy X Therapy Y Therapy Z 85 78 79 79 81 83 84 68 75 67 75 74 Do these results suggest that the different therapies have different effects on mental health? (Use the .05 level.) Note: we have entered the data in SPSS and obtained some descriptive statistics from the three groups. Refer to Table 1 at the end of this question. Use these descriptives to calculate the variances within (d) and between groups (e) and use these to calculate the F ratio. a) Define populations of interest, Ho and Hi [2 marks] b) What is the comparison distribution? [1 mark] c) What is the cut-off sample score on the comparison distribution at which the null hypothesis should be rejected? [1 mark] d) Calculate S within ? [1 mark] e) Calculate Sbetween ? [1 mark] f) What is your conclusion? [1 mark]Table 1: Descriptive statistics for question 3: Descriptives score 95%% Confidence Interval for Mear Mean Sid. Deviation Sid, Error Lower Bound Upper Bound Minimum Maximum 1.0 78.7500 8.26136 4.13068 85.6043 91.8957 35100 2.0 75.5000 5.56776 2.78388 66.6404 84.3596 68.00 81 00 3.00 77.7500 4.11299 2 05649 71.2053 84.2947 74.00 83 00 Total 12 77.3333 5.80491 1.67573 73.6451 81.0216 67.00 85.00 3 "Untitled? [DataSet2) - IBM SPSS Statistics Data Editor O X File Edit View Data Transform Arlyze Direct Marketing Graphs Litities Add-ons Window Help H $ Visible: 2 of 2 Variables score Group wil 85 00 1.00 79 00 1.0 84 00 1 0 87.00 78 00 2 00 81 00 2 00 2 00 75 00 2 00 3 00 10 83 00 3 00 11 75 00 3.00 12 74 00 3.00