The 2*2 design here refers to an experimental design in which there are 2 levels of one factor and 2 levels of another factor.
For instance, in a study to determine the effect of diet and exercise on weight loss, diet might have 2 levels (i.e., healthy and unhealthy diet) and exercise might also have 2 levels (i.e., regular exercise and no exercise). The combinations of these two factors yield 4 conditions (i.e., healthy diet with regular exercise, healthy diet with no exercise, unhealthy diet with regular exercise, and unhealthy diet with no exercise).
Therefore, in this case, we can see that factor A (it could be diet or exercise in the example given) has 2 levels. This is what is referred to as kA.
Now, given that the total number of participants is 40, and they are equally distributed across all conditions, we need to determine the number of participants in the first level of factor A, which is referred to as nA1.
Since there are 4 conditions (2 levels of factor A multiplied by 2 levels of the other factor), and 40 participants, each condition will have 40 divided by 4, which equals to 10 participants.
So, we find that kA is 2 and nA1 is 10. Therefore, the correct option is C. kA=2, nA1=10.