# 10_03_11ans - STAT 409 Examples for 10/03/2011 Fall 2011 1....

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STAT 409 Examples for 10/03/2011 Fall 2011 1. A scientist wishes to test if a new treatment has a better cure rate than the traditional treatment which cures only 60% of the patients. In order to test whether the new treatment is more effective or not, a test group of 20 patients were given the new treatment. Assume that each personal result is independent of the others. Trying to decide: cure rate p 0.60 vs. p > 0.60. a) If the new treatment has the same success rate as the traditional, what is the probability that at least 14 out of 20 patients (14 or more) will be cured? P ( X 14 | p = 0.60 ) = 1 – CDF ( 13 | p = 0.60 ) = 1 – 0.750 = 0.250 . b) Suppose that 14 out of 20 patients in the test group were cured. Based on the answer for part (a), is there a reason to believe that the new treatment has a better cure rate than the traditional treatment? If p = 0.60, then 25% of all possible samples would have 14 or more patients cured (out of 20). Thus, it is not unusual to see 14 out of 20 patients cured for a treatment that cures 60% of the patients. We have no reason to believe that the new treatment has a better cure rate than the traditional treatment if X = 14 . c) If the new treatment has the same success rate as the traditional, what is the probability that at least 17 out of 20 patients (17 or more) will be cured?

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## This note was uploaded on 10/13/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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10_03_11ans - STAT 409 Examples for 10/03/2011 Fall 2011 1....

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