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1) A plant science student wishes to determine factors that influence the prevalence of Medusahead (an invasive annnual grass) on rangelands in eastern Oregon. Soil test results from 20 sites showed a positive correlation between the number of Medusahead present and naturally occuring levels of soil nitrogen. Can he conclude that high nitrogen fertility causes an increase in the prevalence of Medusahead? Explain your answer.
2) Consider how the factors below might influence your choice of plot size in an experiment. For each comparison, circle the scenario that would favor a larger optimum plot size.
a) Border effects due to treatments: Irrigation vs Planting density
b) Experimental material: Douglas fir trees vs Wheat crop
c) Stage of research: Exploratory study vs On-farm demonstration
d) Soil variability: Uniform vs Heterogeneous
3) Which of the following is NOT a necessary assumption for a valid ANOVA? (choose one)
a) The errors (residuals) are independent
b) The observed values (Y (^) ij ) are normally distributed
c) The errors for all treatment groups have a common variance
d) The main effects in the model are additive
8 pts
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4) You have just been hired by a seed company to evaluate the effectiveness of five fungicide treatments on the yield of oats. Last year, they conducted a similar experiment using a standard plot size, and obtained a standard deviation for yield of 15 bushels/acre. They would like to be able to detect differences of 30 bushels/acre, 90% of the time using an alpha level of 0.05. You plan to continue to use the standard plot size to make best use of available supplies and equipment. Will 6 replicates (blocks) be sufficient to attain the precision and power desired for this experiment?
5) A colleague of yours is about to conduct a small field experiment on a uniform piece of land. He is planning to use a Randomized Complete Block Design, because that is the most common way to design a field experiment. Remembering the principle that one should use the simplest experimental design that is appropriate, you suggest that he should consider using a Completely Randomized Design. He is not convinced. What additional arguments could you make to support the use of a CRD?
16 pts
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7) Four varieties of corn were tested for yield in a Completely Randomized Design.
a) Fill in the boxes to complete the ANOVA.
As CRD Source DF SS MS F Total 19 6568 Variety 1016
b) Based on the results, are there significant differences among the varieties at the = 0.05 probability level? What is your proof? (use the tables at the back of this exam)
c) What is the standard error of a variety mean?
8 pts
14 pts
8 pts
F Distribution 5% Points Student's t Distribution
- df 1 2 3 4 5 6 7 df 0.4 0.2 0. Denominator Numerator (2-tailed probability) - 1 161.45 199.50 215.71 224.58 230.16 233.99 236.77 1 1.376 3.078 12. - 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 2 1.061 1.886 4. - 3 10.13 9.55 9.28 9.12 9.01 8.94 8.89 3 0.978 1.638 3. - 4 7.71 6.94 6.59 6.39 6.26 6.16 6.09 4 0.941 1.533 2. - 5 6.61 5.79 5.41 5.19 5.05 4.95 4.88 5 0.920 1.476 2. - 6 5.99 5.14 4.76 4.53 4.39 4.28 4.21 6 0.906 1.440 2. - 7 5.59 4.74 4.35 4.12 3.97 3.87 3.79 7 0.896 1.415 2. - 8 5.32 4.46 4.07 3.84 3.69 3.58 3.50 8 0.889 1.397 2. - 9 5.12 4.26 3.86 3.63 3.48 3.37 3.29 9 0.883 1.383 2.
- 10 4.96 4.10 3.71 3.48 3.33 3.22 3.14 10 0.879 1.372 2.
- 11 4.84 3.98 3.59 3.36 3.20 3.09 3.01 11 0.876 1.363 2.
- 12 4.75 3.89 3.49 3.26 3.11 3.00 2.91 12 0.873 1.356 2.
- 13 4.67 3.81 3.41 3.18 3.03 2.92 2.83 13 0.870 1.350 2.
- 14 4.60 3.74 3.34 3.11 2.96 2.85 2.76 14 0.868 1.345 2.
- 15 4.54 3.68 3.29 3.06 2.90 2.79 2.71 15 0.866 1.341 2.
- 16 4.49 3.63 3.24 3.01 2.85 2.74 2.66 16 0.865 1.337 2.
- 17 4.45 3.59 3.20 2.96 2.81 2.70 2.61 17 0.863 1.333 2.
- 18 4.41 3.55 3.16 2.93 2.77 2.66 2.58 18 0.862 1.330 2.
- 19 4.38 3.52 3.13 2.90 2.74 2.63 2.54 19 0.861 1.328 2.
- 20 4.35 3.49 3.10 2.87 2.71 2.60 2.51 20 0.860 1.325 2.
- 21 4.32 3.47 3.07 2.84 2.68 2.57 2.49 21 0.859 1.323 2.
- 22 4.30 3.44 3.05 2.82 2.66 2.55 2.46 22 0.858 1.321 2.
- 23 4.28 3.42 3.03 2.80 2.64 2.53 2.44 23 0.858 1.319 2.
- 24 4.26 3.40 3.01 2.78 2.62 2.51 2.42 24 0.857 1.318 2.
- 25 4.24 3.39 2.99 2.76 2.60 2.49 2.40 25 0.856 1.316 2.
- 26 4.23 3.37 2.98 2.74 2.59 2.47 2.39 26 0.856 1.315 2.
- 27 4.21 3.35 2.96 2.73 2.57 2.46 2.37 27 0.855 1.314 2.
- 28 4.20 3.34 2.95 2.71 2.56 2.45 2.36 28 0.855 1.313 2.
- 29 4.18 3.33 2.93 2.70 2.55 2.43 2.35 29 0.854 1.311 2.
- 30 4.17 3.32 2.92 2.69 2.53 2.42 2.33 30 0.854 1.310 2.
- d
