I am looking at a question, and it seems that the questions is making some assumptions and that they are providing extra information that is not necessary.

Here is the question:

Consider a $2\times 2$ factorial experiment. How many replications are required to estimate the interaction beta to within 2 units with a $90\%$ confidence interval. (Assume that the standard error of the estimate of the interaction beta is approx. : 3)

This is saying 2 by 2 factorial, but does not state the levels for each of the factors. Not sure how to know how many replications. I know that the formula $2^k,$ like $2^2 =4,$ gives us all the cells hence all the possibilities assuming 2 levels. But not sure if this is correct, but the question seems to be asking in regards to the interaction, and I guess we have to go through all the possibilities to find the interaction.

Is my interpretation correct? I would appreciate an explanation on replication.



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