April 29 - May 1, 2002Statistics 512 Final Exam Spring 2002Statistics 512Final ExamApril 29 - May 1, 2002This is a take home exam. The following rules apply.1. You may use any textbook, including textbooks on the Web.2. You may use any statistical software.3. Answer the questions on the exam paper in the space provided. Labeled computer output should be attached as needed. You may alsoattach additional pages of computations for any problem, but I will check these only if you direct me to them.4. You may not seek help from any person except Prof. Altman and Lan Wang. This includes assistance from internet sources such as e-mail, bulletin boards and chat rooms.5. Since students will be taking the exam at any time during the week, you may not discuss this exam with anyone until Friday May 3. 6. Failure to comply with items 4 or 5 could lead to reduction in your grade, or disciplinary action.7. When you have completed the exam, slide it under my door. I have read the rules above and agree to comply with them.Signature ________________________________________________Name (printed) ___________________________________________1Statistics 512 Final Exam Spring 20021. Ozone has become an important air pollutant, with many adverse effects. Ozone is known to affect growth of many plant species. However, even within species, some varieties show more sensitivity than others, indicating a genetic susceptibility. As well, other factors such as soil moisture may affect ozone sensitivity.In a laboratory study of the effects of soil moisture and ozone on lettuce, 3 varieties were selected from the 28 available, based on genetic susceptibility to ozone (high, medium, low).To maintain the ozone level, the plants must be grown in special chambers. Only one ozone level can be used in each chamber. However, the soil moisture level can be controlled by the use of special pots.The response variable is leaf dry weight, which is a measure of yield of this leafy vegetable. Ozone will be maintained at 30, 50 or 80 ppb. The soil moisture treatments are: constant moisture and fluctuating moisture on a dry/damp cycle. One plant from each variety is used as the sampling unitThe objectives of the study are:1. to assess the effects of ozone and soil moisture on leaf dry weight2. to determine if there is an interaction between ozone and soil moisture3. to determine if there are significant differences in the way that the varieties of lettuce response to the ozone and soil moisturea. Fill out the following table regarding the factors:Name of treatment Categorical or Quantitative Fixed or Randomozonemoisturevariety2Statistics 512 Final Exam Spring 2002b. The investigator is considering 2 designs:A. There will be 18 chambers in all, with 6 chambers at each level of ozone. Each chamber will hold 3 pots with the same moisture treatment. Each pot will hold one plant.All 3 varieties will be placed in each chamber.B. Each pot will hold 1 plant. Each chamber will have one variety of plant only. There will be 27 chambers in all, with 3 chambers of each variety at each level of ozone.Each of the designs above is a split plot experiment with 54 plants. Fill out the following table. Include the following factors: ozone, moisture, variety and all of the 2 and 3-way interactions of these 3 factors.Design A Experimental Unit Blocking factor (if any) Factors Whole plot SubplotDesign B Experimental Unit Factors Whole plot Subplot3Statistics 512 Final Exam Spring 2002c. The random effects of the blocking factors creates correlation among observations. Fillin the following Table for the 2 most highly correlated observations with the stated effects.Observation Correlated Design A (yes/no)Correlated Design B (yes/no)same level of ozone, moisture and varietydifferent levels of ozone, same levels of moisture andvarietysame levels of ozone, different levels of moisture,same varietysame level of ozone, same level of moisture, different varietysame level of ozone, different level of moisture, different variety4Statistics 512 Final Exam Spring 2002d. Major interest in this experiment focuses on the ozone by moisture interaction within variety. Which design provides the most information about this? Justify your answer?e. Another major focus of this experiment is the ozone by moisture by variety interaction.Which design provides the most information about this? Justify your answer?5Statistics 512 Final Exam Spring 2002f. The unit supervisor points out that use of the chambers is very expensive. Each chamber can hold many pots of plants. She suggests that the experiment can be run with only 9 chambers, 3 at each level of ozone. Explain how to design the experiment so that it is a split plot design with 54 plants in all. Call this Design C.g. Is Design C more or less powerful than Design A for detecting Ozone by moisture interaction? Explain your answer.6Statistics 512 Final Exam Spring 20022. For a nutrition project, students investigated the effect of time of meal on glucose response. They provided a pasta dinner for 6 subjects at each of 0200, 0600, 1000, 1400, 1600 and 2000 (on a 24 hour clock). The serum glucose measurement for each subject was taken prior to the meal time, and then at intervals following the meal. Most of the subjects were measured at 10 times.Data for this problem are on the class Web page. The columns of data are:Glucose - the serum glucose levelTime - the measurement times coded from 1 to 10Subject - subject coded from 1 to 6 for each start time (36 subjects in all)Start - start time of the meal on a 24 hour clocka. What are the fixed and random factors for this study?b. Subject should be coded as subject(start) because different subjects were used for each dinner time. Run an analysis which allows for time series error within subject. Is the time series error statistically signficant?7Statistics 512 Final Exam Spring 2002c. The SAS statement:MODEL Y=A B/OUTPRED=filename;saves all of the original data plus predicted values (for the fixed effects of the model) in SAS file "filename". Add this statement to your analysis, and then obtain an interaction plot of START by TIME, so that you can assess the shape of the response curves. Do they appear to be linear? (Please include your curve in the analysis.) You may need to recode the start times in order to obtain unique plotting symbols.d. Based on your analysis, test for the statistical significance of the following