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10. Use the applet to determine what proportion of your 1000 simulated random assignments were the results as (or more) extreme as the actual study (which, youâll recall, saw a 0.467 difference in improvers). This is your p-value. Interpret this p-value, including what is meant by the phrase âby chance aloneâ in this context. 11. Is your p-value small enough so that you would consider an difference in the observed proportion of improvers of 0.467 or more surprising under the null model that dolphin therapy is not effective? Does this give strong evidence that the dolphin therapy is effective in treating depression in patients similar to those in the study? 12. Is it reasonable to draw a cause-and-effect conclusion between dolphin therapy and improvement or not in depression symptoms? Explain why or why not. 13. Is it reasonable to generalize your conclusion to all people who suffer from depression? Explain why or why not. Further Exploration What if the study had found the same overall proportion of improvers, but with the group proportions closer together? More specifically, suppose that the actual data had turned out with 2 fewer improvers in the dolphin therapy group and 2 more improvers in the control group. 14. How will this affect our analysis, and the p-value, and the conclusion? First make a conjecture, and explain your reasoning. 15. Then investigate this question with a simulation. [Hints: Think about how the two-way table will change. Then use your earlier simulation results but explain what you are doing differently now to find the approximate p-value.] Explain why your answers (about how the strength of evidence against the null model changes when the group difference is not as large) make intuitive sense. June 27, 2014 MAA PREP workshop 68