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MidtermExam2_2008_Solutions

# MidtermExam2_2008_Solutions - CHEN 3010 Applied Data...

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CHEN 3010 Applied Data Analysis Fall 2008 Name:________________________________ Midterm Examination 2 ¾ 120 minutes ¾ 100 points (points for each problem shown in parentheses beside the problem number) ¾ open book and notes ¾ calculator allowed (and needed) ¾ do all work on blank sheets or graph paper provided and start each problem on a new sheet ¾ order your work sheets and staple them behind this exam document when you turn in your exam ¾ time will be of the essence on this exam – attempt the problems you know best first, and move from problem to problem quickly – if you get stuck on a problem, move on and return to it later – you will not likely have time to "re-learn" the material during the exam On my honor, as a University of Colorado at Boulder student, I have neither given nor received unauthorized assistance on this work. ______________________________________ (sign on this line) 1) (15 pts) You work for a small start-up pharmaceutical company and are preparing batches of an important protein drug to be used in FDA trials. You need 4 successful batches to ship to the FDA. The company claims that the probability of getting a successful batch is 0.25 (p=0.25). You believe that this is low and the actual probability of getting a successful batch is greater than 0.25. You go about preparing the 4 batches and find that the 7 th batch you make is the 4 th successful batch. Can your claim that the p > 0.25 be supported ( α = 0.05)? Solution: Since we need 4 successful batches and we are interested in how many trials required to get these 4 batches this is a negative binomial distribution. We want to see how probable is it for use to get the 4 th successful batch on the 7 th batch we make. The company claims that the probability of success is 0.25 but we think it is higher. Thus, we can set up the following hypothesis and test it based upon the fact that we got the 4 th successful batch on the 7 th batch we made: ܪ :݌ൌ0.25,ܪ :݌൐0.25 Essentially what we are trying to find is how rare is it for us to get the 4 th success on the 7 th batch if the true success rate is 0.25. Thus, we are looking at the negative binomial distribution: ݂ሺݔሻ ൌ ቀ ݔെ1 ݎെ1 ቁ ሺ1 െ ݌ሻ ௫ି௥ ݌ where x is the number of trials required to obtain exactly r successes. To support the alternate hypothesis we must show that the probability of getting 4 successes on 4, 5, 6,

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CHEN 3010 Midterm Exam 1 Page 2 or 7 batches is less than an alpha value of 0.05. Here are the non-cumulative and cumulative probabilities (using the negative binomial distribution function above) for x = 4 to x = 7:
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MidtermExam2_2008_Solutions - CHEN 3010 Applied Data...

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