Week_10_Practice_Problems

Week_10_Practice_Problems - Week 10 Practice Problems These...

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Week 10 Practice Problems These problems involve tests of significance that make use of the central limit theorem and the likelihood ratio. 1. Suppose 2 1 ~ W χ and . Explain why ~( 0 , 1 ) ZG () ( | | PW d P Z d ≥= ) [we will use this result below] 2. In assessing a new treatment, 200 patients are tested and the treatment is successful 134 times. The standard treatment has a success rate of 60%. Is there any evidence that the new treatment has a different success rate? Assume a binomial model is appropriate. a) Carry out a test of significance using an approximation based on the central limit theorem. b) Carry out a likelihood ratio test. Use the result in question 1 to get a good approximation to the p-value. c) How do the conclusions of the two tests compare? 3. The number of flaws in a glass sheet can be modeled by a Poisson random variable. Suppose a change is proposed to the production process. To see if the change affects the number of flaws, a experiment is carried out. Twenty sheets of glass are produced
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Week_10_Practice_Problems - Week 10 Practice Problems These...

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