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6. Combine your results with your classmates by constructing a dotplot of the differences in improvement proportions (dolphin group minus control group). 7. Does it appear that the observed value of this statistic (namely, 0.467) would be unlikely to occur if there really were no effect of the dolphin therapy? Explain. Remember the p-value is the probability we would observe a statistic at least as large as we did in our study, assuming the null hypothesis was true. By shuffling and dealing the cards, we are simulating a true null hypothesis. We are simulating a random assignment of the 13 subjects that actually improved to each group. 8. What proportion of the results from your class had a difference in the proportion of improvers of 0.467 or larger? This is your p-value. Provide a detailed interpretation of this p-value. Be sure to explain what is meant by âby chance alone,â keeping in mind what was randomized in this study. 9. Based on the class results, what is your preliminary conclusion about the effectiveness of swimming with dolphins in improving peoplesâ depression symptoms? Explain the reasoning process behind this conclusion. We really need to carry out this simulated random assignment process hundreds, preferably thousands of times. This would be very tedious and time-consuming with cards, so letâs turn to technology. To do this, use the âDolphin studyâ applet found at: http://www.rossmanchance.com/ISIapplets.html. Check the âShow Shuffle Optionsâ x boand then press the âShuffleâ button. Notice that the applet does what you have done: shuffle the 30 cards and deal out 15 for the âdolphin therapyâ group, separating cards by color. The applet also determines the 2Ã2 table for the simulated results (check the Show table box on the left) and creates a dotplot of the shuffled difference in conditional proportions. Now press the âShuffleâ button four more times. Then increase the âNumber of Shufflesâ to 995 and press the âShuffleâ button. This produces a total of 1000 repetitions of the simulated random assignment process. June 27, 2014 MAA PREP workshop 67