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MidtermExamSolns

# MidtermExamSolns - Spring 2007 STA 4702/5701 Midterm Exam#1...

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Spring 2007 - STA 4702/5701 - Midterm Exam #1 Solutions Name: Directions : Please read all problems carefully. The exam is worth a total of 200 points. The points for each problem are shown to the left. Good luck! 1. (15) For each of the data sets described below indicate whether the data are non-random missing , missing at random , or missing completely at random by writing NRM, MAR, MCAR in the space provided. (a) A survey was taken by telephone by paid staff members to estimate the proportion of US voters who would consider voting for Hilary Clinton in the upcoming presidential election. The survey was taken mostly during regular working hours. The proportion of respondents who were women aged 25 to 35 was 85%. The estimated proportion in the general US population for voters of this demographic is around 48%. solution MAR. For age and sex, the probability of being missing (missingness) doesn’t depend on the answer. Data to reconcile the sample proportions with the population proportions can be simulated based on the respondents who did answer. (b) Researchers were measuring toluene concentrations in a random sample of small springs in an area near a petroleum factory. The instrument they were using had a detection limit of 0.001 ppb, so measurements below this concentration were censored by the instrument, i.e., reported as “BDL” (below detection limit). Larger springs tended to have a higher probability of high concentrations and so a lower probability of being BDL, but to have the same probability of being sampled as smaller springs. That is, the size proportions in the sample appeared to be representative of the size distribution in the area. solution NRM. This missingness depends on both Y (concentration) and X (size of stream). (c) A scientist was running test tubes of DNA samples to look for the occurrence of a rare genotype in a population of turtles in the Galapagos Islands. The test tubes were arranged in order of sample number. The sample was a random sample from 5 islands. While preparing the test tubes for analysis, her sleeve caught on the corner of one of the trays and 50 tubes out of 300 were knocked over and lost. solution MCAR. The missingness does not depend on either X or Y . 2. Professors at a certain public university are rated by their students on a scale of 1 to 10, with one being ‘horrible’ and 10 being ‘fantastic’. A faculty member who consistently receives low scores believes that the ratings are determined by how difficult the course is. She believes that students will rate professors lower if the material is difficult. Scores of difficulty range from 0 to 5, where 5 is the most difficult. Below is a regression model of 60 average faculty 1

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scores for different courses by the average difficulty rating received. The SAS output is shown below: Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 55.33573 55.33573 82.96 <.0001 Error 58 38.68592 0.66700 Corrected Total 59 94.02165 Root MSE 0.81670 R-Square 0.5885 Dependent Mean 3.30884 Adj R-Sq 0.5814 Coeff Var 24.68234 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value
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