midterm2-soln - F-2011 STAT 410/510 Midterm Exam 2 NAME:

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Unformatted text preview: F-2011 STAT 410/510 Midterm Exam 2 NAME: _____________________________ 1. The following data is concerning the proportion of coal miners who exhibit symptoms of severe pneumoconiosis and the number of years of exposure. The data are shown below: Years of exposure Severe cases Miners 5.8 0 98 15.0 1 54 21.5 3 43 27.5 8 48 33.5 9 51 39.5 8 38 46.0 10 28 51.5 5 11 A partial SAS output is printed out below: Standard Wald Parameter DF Estimate Error Chi-Square Pr > ChiSq Intercept 1 -4.7964 0.5686 71.1612 <.0001 years 1 0.0935 0.0154 36.7079 <.0001 a) Write a generalized linear model that is to be appropriate. Obtain the sample proportion of severe cases occurred and the predicted proportion from the model. Sketch an overlay scatter plot to show the sample proportion and the predicted proportion of severe cases occurred to show the linear model fit. Answer) { } { } Obs years y n response pie 1 5.8 0 98 0 0.01400 2 15 1 54 0.018518519 0.03247 3 21.5 3 43 0.069767442 0.05803 4 27.5 8 48 0.166666667 0.09742 5 33.5 9 51 0.176470588 0.15903 6 39.5 8 38 0.210526316 0.24886 7 46 10 28 0.357142857 0.37820 8 51.5 5 11 0.454545455 0.50421 F-2011 STAT 410/510 Midterm Exam 2 NAME: _____________________________ b) Obtain the odds ratio and interpret this number using the language of this problem. If the exposure time increases by 10 years, then what is the odds ratio would be? What does it tell you? Answer) exp(.0935) = 1.098011 Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits years 1.098 1.065 1.132 Every additional year of exposure increases the odds of contracting a severe case of pneumoconiosis by approximately 10%. If the exposure time increases by 10 years, then the odds ratio becomes . This indicates that the odds becomes more than double with a 10-year exposure. c) When is the estimated median time of exposure in years that is, the time of exposure for which 50% of the coal miners are expected to exhibit symptoms of severe pneumoconiosis? Answer) years of exposure d) By assuming that large-sample inferences are applicable, obtain an approximate 95% CI for . 1 Convert this confidence interval into one for the odds ratio. Interpret this latter interval. Estimated Probability 0.0 0.2 0.4 0.6 0.8 1.0 years 10 20 30 40 50 60 Scatter plot fitted vs months F-2011 STAT 410/510 Midterm Exam 2 NAME: _____________________________ Answer) ( ) It is 95% confident that the true odds of the number of symptoms of severe pneumoconiosis...
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midterm2-soln - F-2011 STAT 410/510 Midterm Exam 2 NAME:

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