An experiment was conducted to compare six different management techniques (such as pruning, spraying and fertilizing) for apple trees with respect to yield. Each apple tree represents an experimental unit and the trial was layed out as a completely randomized design with 5 replications for each management tech- nique. All the trees underwent the same management practice before the trial. For each tree the yield in bushels

(c) for the four-year period preceding the trial is available. At the end of the four-year experimental period, the yield in pounds of apples (y) is obtained for every tree. Suppose the partial SAS Proc GLM printout is as follows:

(i) Are there differences among the management techniques (treatments)? (ii) Has the use of a covariate been successful in reducing the variance for treatment comparisons? (iii) Suppose the supplementary information were not available. How would you test Ho: T1 = 72 = ... = 76? (iv) Suppose 1. 10, 2. = 8. (xij - i.) 12, 3. = 9, 4. = 10, s. 13, 6. = 20. What is the standard error of the comparison "treatment 1 vs. remaining treatments?"

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Source Type ISS Type III SS Treatments 40 60 Prev. Yield 26 26 Error 46 Total 112