Final answer:
The assertion that a controlled factor set at multiple levels is of no interest to the researcher is false; researchers control factors to explore their effects on the outcome of an experiment.
Step-by-step explanation:
The statement that a factor is of no interest to the researcher when it is controlled and set to three levels is false. The correct option is C: The statement is false because a factor that is controlled and set at various levels is a factor of interest to the researcher. When a researcher controls a factor and sets it to different levels, it indicates that they are assessing the effect of these levels on the outcome of the experiment. The number of levels set for a factor does not necessarily correlate with the researcher's interest in it; rather, it helps in understanding the relationship between the factor and the response variable more comprehensively. The degree of control and the number of levels can vary depending on the design of the study and the specific questions the researcher aims to answer. For instance, if one is studying the effect of fertilizer on plant growth, setting zero (control), medium, and high levels of fertilizer allows the researcher to observe the response of plant growth at no, moderate, and high input levels. This helps in examining whether there is a linear relationship, a threshold effect, or a saturation point regarding the fertilizer's effect.