A horticulturist employed by a large florist is assigned responsibility for determining the effect of length of storage and conditioning time after storage on the height of Easter lilies at first bloom. Tall lilies are in great demand and sell at a premium price. Two storage periods (SP1 and SP2) and two conditioning times after storage (T1 and T2) were chosen for this experiment. The heights of three plants were measured at each of the four combinations of storage period and conditioning time, and the data is given in the following table. It was felt that this amount of replication would give an adequate estimate of the plant height at each of the experimental conditions. All other variables were held constant, and the 12 plants were randomly distributed around the greenhouse to ensure that any unanticipated changes would not bias the results of the experiment.
(1) Hand-calculate (with detailed procedures/formulas) the effects of the two main factors, as well as their interaction effect, and interpret these effects.
(2) Conduct a DOE study in Minitab, and provide the main statistical and graphical outputs. What conclusion can you make based on these results.
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(3) Under what conditions should Easter lilies be stored to maximize height at first bloom?
Table. Height of Easter lilies at first bloom
|Conditioning Time||Storage Period||Height (Inches)|
|T1||SP1||28, 26, 30|
|T1||SP2||49, 37, 38|
|T2||SP1||31, 35, 31|
|T2||SP2||37, 37, 29|