RESEARCH SCENARIO 3: Mindfulness Meditation:You are a clinical psychologist working in a community mental health center and you review the literature on the effects of psychotherapy on quality of life. You find that individuals who undergo 16 weeks of standard psychotherapy improve by 10 points ( = 10, s = 3.5) on a validated quality of life measure. You believe that by adding a mindfulness meditation component to the existing forms of psychotherapy, you can improve quality of life by more than 10 points (>10). You observe a random sample of 40 patients who experienced psychotherapy and mindfulness meditation. Your data indicates that their average QoL score improves by 11 points, on average.Run a one-tailed hypothesis test, with alpha = 0.0513. (Step 1): Identify the two comparison populations.1 = ?2 = ?14. (Step 2): State the null & research hypothesis (in symbols AND words)15. (Step 3): State the parameters (mean and standard error) of the comparison distribution. = ?sM = ?16. (Step 4) Calculate the critical values (alpha level & z-critical). Identify rejection region (in terms of z-scores, when would you reject H0?).17. (Step 5) Calculate the test statistic (z-observed)18. (Step 6) Is z-observed greater than or less than your z-critical (in mathematical terms)? State your research decision and interpret briefly (in plain language).19. If we changed the alpha level to p < .01, what would the new z-crit be?20. Would changing to the z-crit as in #19 (above) change our decision about the null? If so, how?MathStatistics and Probability PSYCH 2220
