For each problem, you will have to determine the design. Your design choices are Randomized Block Split Plot, Split Plot, ANCOVA, Crossover, Repeated Measures, Nested Design, Latin Square, Random Effects, Fixed Effects, and Mixed Effects (in that order). So if it is a Nested design with fixed treatments, you will answer Nested Design, not Fixed Effects

1. An experiment is to compare the yield of three varieties of oats and four different levels of manure. Suppose 6 farmers agree to participate in the experiment and each will designate a farm field for the experiment. Each farm will be divided into three equal-sized pieces and each piece is assigned a variety of oat. Each whole piece is divided into 4 smaller pieces and the four levels of manure are randomly assigned to the 4 smaller pieces.