An agricultural experiment station wishes to determine the yields of five newly introduced varieties of corn using a completely randomized design (CRD). Each type of corn is planted to four plots of land with equal fertility and grown under uniform cultural management practices, and the yields, in units of 100 bushels, are shown below. In view of these results, can we conclude that the mean yields of the five varieties of corn are the same using the 5% level of significance? Variety Plots 1 2 3 4 A 19 18 18 20 B 25 23 26 24 C 10 14 14 19 D 21 20 19 24 E 14 14 16 17 1. Justify the use of the completely randomized design. What are the requisites of the CRD? Are they satisfied in the experiment? 2. Propose a possible layout of the experiment. 3. State the statistical linear effects model and define the terms in the context of the experiment. 4. State the hypotheses of interest ( in terms of the parameters in the linear model in #3) and propose a test statistic to test the null hypothesis. Ho: ______________________________________________________________________ Ha: ______________________________________________________________________ 5. Carry out the analysis of variance using manual computations (show all solutions) and summarize your results in the ANOVA table. Conduct the appropriate test proposed in #4 and interpret your results. Define the scope of your conclusions based on whether your model is fixed or random. 6. Do the analysis using STAR or any software available. Generate the variety means and 95% confidence interval about the means. 7. Calculate the coefficient of variation and adequacy of fit of the model. Interpret these measures in the context of the experiment. 8. Describe an experiment in your field of specialization where CRD may be applied. Include in your description why the use of CRD is justified.
An agricultural experiment station wishes to determine the yields of five newly introduced
varieties of corn using a completely randomized design (CRD). Each type of corn is planted to
four plots of land with equal fertility and grown under uniform cultural management practices,
and the yields, in units of 100 bushels, are shown below. In view of these results, can we
conclude that the mean yields of the five varieties of corn are the same using the 5% level of
significance?
Variety Plots
1 2 3 4
A 19 18 18 20
B 25 23 26 24
C 10 14 14 19
D 21 20 19 24
E 14 14 16 17
1. Justify the use of the completely randomized design. What are the requisites of the
CRD? Are they satisfied in the experiment?
2. Propose a possible layout of the experiment.
3. State the statistical linear effects model and define the terms in the context of the
experiment.
4. State the hypotheses of interest ( in terms of the parameters in the linear model in #3)
and propose a test statistic to test the null hypothesis.
Ho:
______________________________________________________________________
Ha:
______________________________________________________________________
5. Carry out the analysis of variance using manual computations (show all solutions) and summarize your results in the ANOVA table. Conduct the appropriate test proposed in #4 and interpret your results. Define the scope of your conclusions based on whether
your model is fixed or random.
6. Do the analysis using STAR or any software available. Generate the variety means and
95% confidence interval about the means.
7. Calculate the coefficient of variation and adequacy of fit of the model. Interpret these
measures in the context of the experiment.
8. Describe an experiment in your field of specialization where CRD may be applied.
Include in your description why the use of CRD is justified.
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