A medical research team wishes to evaluate two different

Chapter 0, Problem 6.79

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A medical research team wishes to evaluate two different treatments for a disease. Subjects are selected two at a time, and then one of the pair is assigned to each of the two treatments. The treatments are applied, and each is either a success (S) or a failure (F). The researchers keep track of the total number of successes for each treatment. They plan to continue the chance experiment until the number of successes for one treatment exceeds the number of successes for the other treatment by 2. For example, they might observe the results in the table below. The chance experiment would stop after the sixth pair, because Treatment 1 has 2 more successes than Treatment 2. The researchers would conclude that Treatment 1 is preferable to Treatment 2. Suppose that Treatment 1 has a success rate of .7 (i.e., P(success) .7 for Treatment 1) and that Treatment 2 has a success rate of .4. Use simulation to estimate the probabilities in Parts (a) and (b). (Hint: Use a pair of random digits to simulate one pair of subjects. Let the first digit represent Treatment 1 and use 17 as an indication of asuccess and 8, 9, and 0 to indicate a failure. Let the seconddigit represent Treatment 2, with 14 representing asuccess. For example, if the two digits selected to representa pair were 8 and 3, you would record failure forTreatment 1 and success for Treatment 2. Continue to selectpairs, keeping track of the total number of successesfor each treatment. Stop the trial as soon as the number ofsuccesses for one treatment exceeds that for the other by2. This would complete one trial. Now repeat this wholeprocess until you have results for at least 20 trials [more isbetter]. Finally, use the simulation results to estimate thedesired probabilities.)a. Estimate the probability that more than five pairs mustbe treated before a conclusion can be reached. (Hint:P(more than 5) 1 P(5 or fewer).)b. Estimate the probability that the researchers will incorrectlyconclude that Treatment 2 is the better treatment.