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# Download Introduction to Chance Models (Section 1.1) Introduction A key step

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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 âby 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 letâs turn to
technology. To do this, use the âDolphin studyâ applet found at:
http://www.rossmanchance.com/ISIapplets.html. Check the âShow Shuffle Optionsâ x boand
then press the âShuffleâ button. Notice that the applet does what you have done: shuffle the 30
cards and deal out 15 for the âdolphin therapyâ group, separating cards by color. The applet
also determines the 2Ã2 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
âShuffleâ button four more times. Then increase the âNumber of Shufflesâ to 995 and press the
âShuffleâ button. This produces a total of 1000 repetitions of the simulated random assignment
process.
June 27, 2014
MAA PREP workshop
67
```
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