The design should be b. A completely randomized design if the experiment is to be conducted with four factors at three levels.
In a completely randomized design, the number of factors can be randomly determined and can be more than two. Also, the experimenter can also set the levels of the independent factors. Therefore in this case where the experiment is conducted with four factors at three levels, the completely randomized design is the most suitable.
On the other hand, a one-way ANOVA design is not suitable for this experiment as it only includes a single independent variable or factor. A two-way ANOVA is an extension of a one-way ANOVA design that considers the influence of only two independent variables on one dependent variable, so this design can also be not used in this case.
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