An experiment was conducted to determine the effect of light and leaf age on the photosynthetic efficiency of a plant. The experiment was conducted as a split plot design with light intensities of 0, 33, and 90 units. The subplots are the sequence number of the first five leaves counted from the top of the plant. The leaf number is proxy for the age of the leaf, with the oldest leaf at the top, etc. There are 15 separate plants, five within each level of light. These are labeled using REP, but Rep = 1 within Light = 0 is a different plant from that within Light = 33. That is, plants play the same role as cones of thread in Example 10.7. This problem is similar to that example. The data are given in Table 10.31.
(a) Test for the existence effects for light and leaf. Assume REP does not interact with these effects.
(b) Assuming that the leaf numbers represent equally spaced ages, determine whether a polynomial response can be used for the effects of light and age.
(c) Perform a lack of fit test.
Example 10.7
The purpose of this experiment is to test the differences in the strengths of sewing thread made by five different manufacturers. Five cones of thread (CONES) were obtained from each of five manufacturers (MANUF). The test consists of passing a specimen of thread through some guide pins (PINS) and measuring the energy (ENERGY) required to rupture the specimen. The lower the required energy, the weaker the thread. In this experiment, 20 specimens of thread were randomly selected from each cone and assigned to one of two guide pin treatments (using two or three pins). The data given in Table 10.19 are the means of the 10 readings for each cone and pin.
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