A research laboratory was developing a new compound for the relief of severe cases of hay fever. In an experiment with 36 volunteers, the amounts of the two active ingredients (factors A and B) in the compound were varied at three levels cach. Randomization was used in assigning volunteers to cach of the nine treatments. The dataon hours of relief follow (dataset in the file relief. csv" where the columns represent Hours of Relief, Factor A Level; Factor B Level; Subject). Factor B (Ingredient 2) Factor A (Ingredient 1) j = 1 j = 2 j = 3 Low Medium High i = 1 Low 2.4 4.6 4.8 2.7 4.2 4.5 2.3 4.9 4.4 2.5 4.7 4.6i = 2 Medium 5.8 8.9 9.1 5.2 9.1 9.3 5.5 8.7 8.7 5.3 9.0 9.4i = 3 High 6.1 9.9 13.5 5.7 10.5 13 5.9 10.6 13.3 6.2 10.1 13.2 4. Is this setup an observational study or an experiment? Write down the corresponding inter pretation for Hij in this scenario 5. Write down the cell-means model and the factor-effects model for this scenario, along with any assumptions and/or constraii 6. Make an interaction plot. Does your graph suggest that any factor effects are present? If so, which ones?