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[Solved] The following data are the treatment means and variance from an experiment where each treatment was randomly and equally allocated to a total of

Question: The following data are the treatment means and variance from an experiment where each treatment was randomly and equally allocated to a total of 32 experimental units. Suppose the experimenter

Trt1 Trt2 Trt3 Trt4
Mean 3 0 1 2
var 5 7 6 7

planned to test the following three hypotheses

  1. \(H_{o}: 3 \mu_{2}=\mu_{1}+2 \mu_{4}\)
  2. \(H_{0}: 2 \mu_{2}=\mu_{1}+\mu_{3}\)
  3. \(H_{o}: \mu_{3}=\mu_{1}\)
  4. \(H_{o}: \mu_{2}=-2 \mu_{1}+\mu_{3}\)
  1. Calculate the MSE (Mean Square Error).
  2. Using a = 0.05, test each of the four hypotheses (two sided).
  3. Which of the four linear combinations of means are contrasts? Why?
  4. Are any pairs of contrasts orthogonal? Which ones and Why?
  5. Find one contrast that is orthogonal to the first contrast (i).
  6. What is the overall type one error a for the simultaneous tests (ii) and (iii).

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Solution: The downloadable solution consists of 5 pages
Deliverable: Word Document


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