The effect of five different ingredients (A, B, C, D, E) on the reaction time of a chemical process is being studied. Each batch of new material is only large enough to permit five runs to be made. Furthermore, each run requires approximately hours, so only five runs can be made in one day. The experimenter decides to run the experiment as a Latin square so that day and batch effects may be systematically controlled. She obtains the data that follow. Analyze the data from this experiment (use 0.05) and draw conclusions. Day

Batch   1                   2                  3                  4                   5
1        A = 24           B = 20         C = 19          D = 24          E = 24
2        B = 17           C = 24         D = 30          E = 27          A = 36
3        C = 18           D = 38         E = 26          A = 27          B = 21
4        D = 26           E = 31         A = 26          B = 23          C = 22
5        E = 22           A = 30         B = 20          C = 29          D = 31  

Required:
a. By hand calculation, analyze the data from this experiment (Use α=0.05), create an ANOVA table, and draw conclusions.
b. Eliminate the factor(s) that shows no significant effect on the response, then "collapse" the design and analyze it again, creating an ANOVA table and drawing conclusions.
c. Analyze each of the three factors separately using one way ANOVA (take one factor at a time for analysis) and make inferences about the residual sum of squares. Why does the residual sum of squares change and how does it affect the F-value and your results?