Stat 505 Assignment 2

Due September 16, 2011
Use any font for comments and explanations, but use courier (or other fixed-width) font for computer input and output. Insert plots near your discussion, not all at the end of the assignment. Don't let R print significance stars.
  1. Fill in the blanks in the following ANOVA table 
    Source          df      SS      MS      F   p-value
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Between groups  __  ______  ______   ____   ______

Within groups  124  76.384  ______
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Total          126  95.212
  2. The isotopic composition of vertebrae bone is known to vary with temperature at which the bone was deposited. Data from a 1994 article in Science by Barrick and Showers (v 265:222-224) provides oxygen isotopic composition for 12 vertebrae bones (Each measured three or more times) from a single Tyrannosauros rex specimen. If compositions are all similar, it would provide evidence that T.rex was warm blooded. If there are strong differences, we would think the dinosaur was cold blooded.
    1. Plot the data and comment on the spread between bones as compared to the spread within bones. Venture an opinion. Warm or cold blooded?
    2. Use ANOVA to evaluate the "warm-blooded" theory. State your hypotheses and your conclusion. Include the ANOVA table.
    3. Discuss: Does your conclusion apply to all T.Rexes?
  3. Levels of fatty acid, CPFA, were randomly assigned to rats to determine its effect on a certain liver protein. Source: Donald A. Pierce, as in Ramsey and Schafer (2002) The Statistical Sleuth p 142.
    1. Plot the data. by treatment group.
    2. Run an ANOVA to see if the levels of CPFA have different means.
    3. Test the hypothesis that the effect of CPFA on protein is linear. Is there a substantial lack of fit?
    4. Note that for each day of the study, one treatment was compared to control. How does this design affect our ability to compare treatment effects? Suggest an alternative design and explain why it is better.
    5. Construct a boxplot of the control values versus day. Is there a pattern in the day on which the protein was measured? If so, can we include day as another predictor?
    6. What do you conclude about the effects of CPFA on the protein? Does it cause decrease in protein? Can the results be extended to the larger population of "all lab rats"?