Setup: 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 four levels for A, and three levels for B. Randomization was used in assigning four volunteers to each of the twelve treatments. The data on hours of relief follow (dataset in the file "relief.csv" where the columns represent Hours of Relief; Factor A Level; Factor B Level; Subject).

Questions:

1. Is this setup an observational study or an experiment? Write down the corresponding interpretation for ij in this scenario.

2. Make an interaction plot with Factor B (Ingredient 2) on the x-axis, and Factor A (Ingredient 1) as the different lines on the graph. Provide your graph. Does your graph suggest that any factor effects are present? If so, which ones?

3. Provide the ANOVA table for this scenario. Include the Sources: Factor A, Factor B, Interaction AB, Error, and Total. Include the columns SS, df, MS, and F.

4. Test whether or not the two factors interact. Use ? = 0.05.

? State your hypotheses.

? Find the value of the test statistic.

? Find the p-value or state the critical region.

? State your decision (Reject H0 or Do Not Reject H0).

? State your conclusion.

5. Test whether Factor A main effects are present. Use the cell means model setup. Use

? = 0.05.

? State your hypotheses.

? Find the value of the test statistic.

? Find the p-value or state the critical region.

? State your decision (Reject H0 or Do Not Reject H0).

? State your conclusion.

6. Test whether Factor B main effects are present. Use the factor effects model setup. Use

? = 0.05.

? State your hypotheses.

? Find the value of the test statistic.

? Find the p-value or state the critical region.

? State your decision (Reject H0 or Do Not Reject H0).

? State your conclusion.

7. Does it make sense in this scenario to consider main effects? Why or why not?