Final Exam, STA 6166, Fall 2007 Instructions: As this is a take-home exam, I expect everyone to work completely on their own. As always all analyses and write-ups are to be your own work. Please show all work in order to get full credit. This includes inserting relevant output from statistical computing software into your write-ups. If a questions asks for short answers, use bullets or lists rather than sentences where feasible. Please be succinct but complete in your answers. Finally, Part I can be handed in anytime between now and 1:55 pm Tuesday December 4. Part II can be handed in anytime between now and 10:00 am Thursday December 13. I will accept only hardcopy; please do NOT email your exam to either me or Nabanita. If you are out of town, send it to someone who can print out a copy and hand it to me or Nabanita. To ensure that all exams have been handed in, I will email a list of individuals whose exams have been received by 8 am December 13. If your name is not on the list you must get me the exam by 10:00 am that day. Part I A) Please read the attached paper by Bell et al. (2005, Science, 308, 1884 and supplementary material; Attachments I and II) and answer the following questions: a. State in words all sets of hypotheses that the authors are interested in testing (note that the authors could be interested in more than one set of hypotheses!) b. Is the research observational or experimental? c. What factors or explanatory variables are they interested in studying for their effects on the microbes? d. What response variables are they measuring on the microbes? e. Describe the population(s) of interest to the researchers (Hint: think in terms of the scope of inference – what group(s) or set(s) do the scientists wish to make inferences about)? f. Describe the sample(s) that were collected, including the method used for selecting the sample. g. Restate all sets of hypotheses in statistical terms, i.e. in terms of the population parameters that are believed to be affected by the treatments. h. Describe the statistical method used to test the hypotheses. Have all the assumptions of the test been met? Explain. B) Suppose you are asked to design an observational study to answer the question: Are undergraduate students on campus more likely to take classes during periods 1, 2, or 3 than undergraduates students who commute to campus? You are to design a strategy for sampling 100 students from each population to test the hypothesis. So, please answer the following questions: a. State the hypotheses to be tested in statistical terms.b. What testing procedure will you use? c. What are the assumptions of the test? d. How will you design the sampling in order to ensure that the assumptions of the test are met? Describe the sampling design you will use. If you are using any lists such as registrar information please describe explicitly what information you are assuming is available for you to use. e. How does your design ensure that the sample is representative of the population being sampled (representative: sample estimates are unbiased for the population parameters being estimated)? Part II A. During a study of the effect of an oil spill on the interstitial marine biota on sandy beaches, a graduate student collected a total of 129 animals in a stretch of beach near Catalina Island in California that had been “oiled”. For each animal measured, the student recorded its species, length, weight, coordinates of the collection location (where on the beach it was found), and the substrate on which it was found (sand, rock, wood, pebbles, etc.). 1. The qualitative variables are … (list them) 2. The quantitative variables are … (list them) 3. The sample consists of … (finish the sentence) 4. Suppose the student plans to test whether the oil spill has decreased the average size (weight and length) of individuals of the most abundant species. a. Describe the population(s) appropriate for the inference from the test. b. Describe the likely hypotheses to be tested. b. Describe the testing procedure that should be used to test the hypotheses you gave. What prior information, if any, is needed to perform this test? B. Suppose a graduate student in your department shows you the following matrix of Pearson correlation coefficients for four variables: X1 X2 X3 X4 X1 1.000 0.83343 -0.87627 0.09951 X2 1.0000 0.77677 0.47300 X3 1.0000 -0.17368 X4 1.00000 1. Which correlation coefficients in the matrix imply that the two variables are highly correlated? 2. Suppose you are told that X2 is a purely categorical variable that was coded as 1, 2, 3, or 4 (rather than names). Is the Pearson correlation coefficient appropriate to look at the strength of the relationship between X2 and the other variables? Explain. C. The following experiment on reproductive fitness in ospreys was conducted back in 1970-1980s. Review the description of the experiment and then answer the following questions.DDT was used extensively in the 1950s and 1960s but its use was banned in 1972. DDT, and its byproducts, was found to persist in the environment well after it was banned. Along with all the other deleterious effects DDT caused in the environment, it also was found to cause thinning of the eggshells of predaceous birds such as the osprey and eagle. As a result the reproductive fitness of the birds was severely compromised. The research question is: Did the ban lead to a recovery by the osprey in their fitness? The dataset contains the results of a field study conducted in New England over several years. Three years were chosen for data collection: 1970, 1976, and 1982. In any given study year, five osprey nests were randomly selected at each of two bay locations (‘MAS’ and ‘Gar’). This gives a total of 30 nests observed in the study. For each year, the selected nests were observed over the season for the reproductive capacity of the nesting pair (ability to hatch chicks, survival of the chicks, successful fledging, etc). At the end of the season, a reproductive fitness index was calculated for each nest. A low value indicates poor fitness and high values indicate good potential for reproduction. Hence data were collected for 6
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